Integral Help
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Calculus Help: ∫ (20x^3)/(1+x^4 )^4 dx - Integration by substitution #Substitution #Integrals
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Calculus Help: ∫ (20x^3)/(1+x^4 )^4 dx - Integration by substitution #Substitution #Integrals

Calculus Help: ∫ (20x^3)/(1+x^4 )^4 dx - Integration by substitution #Substitution #Integrals #Antiderivative #Calculus
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The graph above shows the base of an object. Compute the exact value of the
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The graph above shows the base of an object. Compute the exact value of the

The graph above shows the base of an object. Compute the exact value of the volume of the object, given that cross sections (perpendicular to the base) are squares. #CrossSection #Area #Volume #Integrals
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Calculus Help: A ball of radius 13 has a round hole of radius 9 drilled through its center.
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Calculus Help: A ball of radius 13 has a round hole of radius 9 drilled through its center.

A ball of radius 13 has a round hole of radius 9 drilled through its center. #Radius #Calculus #Integral #Volume #Integrations
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Calculus Help: Calculus Help: If I_n=∫ x^n e^x dx ,n∈NProve that I_n=x^n e^x-nI_(n-1) #Parts
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Calculus Help: Calculus Help: If I_n=∫ x^n e^x dx ,n∈NProve that I_n=x^n e^x-nI_(n-1) #Parts

Calculus Help: If I_n=∫ x^n e^x dx ,n∈NProve that I_n=x^n e^x-nI_(n-1) #Parts #Integrals #Techniques
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Calculus Help: Reverse the order with the order of integration and evaluate ∫ ∫ cos(32π x^6) dx dy
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Calculus Help: Reverse the order with the order of integration and evaluate ∫ ∫ cos(32π x^6) dx dy

#DoubleIntegrals #Integrations #Reversed #Calculus
Calculus Help: An object of mass m is dropped into the sea at the surface. It is subject to a
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Calculus Help: An object of mass m is dropped into the sea at the surface. It is subject to a

An object of mass m is dropped into the sea at the surface. It is subject to a constant gravitational acceleration g and water resistance. (a) (4 points) If the water resistance is proportional to the object's velocity v(t) with coefficient b ≫ 0, so that Newton's second law gives b dv/dt =g- b/m v show that the object's velocity as a function of time t is given by v(t) = mg/b (1-e^(-bt/m)). We take downward to be the positive direction and the object is at rest when it is dropped at t=0. (b) (4 points) If instead the water resistance is quadratic in the velocity, so that Newton's second law gives dv/dt =g- b/m v^2 dt m dv dt find the object's velocity as a function of time t, again assuming that the object is dropped from rest. [Hint: Write Newtons' law as = g(1 − k^2v^2) where k = √b/mg. Then the algebra is a little less messy. After obtaining the final answer in terms of k, remember to replace k by √b/mg.] (c) (2 points) If the object could fall forever under these conditions without hitting the bottom, show that as t→ ∞ the velocity in part (a) approaches terminal velocity v → mg/b. What terminal velocity does the velocity in part (b) approach? #CalculusHelp #Integrals #differentialequations #PartialFractions
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Integral: ∫ cosx cos^2⁡ (sinx)dx ∫ sinx cos^2⁡ (cosx) dx ∫ cosx sin^2⁡ (sinx)dx ∫sinx sin^2⁡(cosx)dx
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Integral: ∫ cosx cos^2⁡ (sinx)dx ∫ sinx cos^2⁡ (cosx) dx ∫ cosx sin^2⁡ (sinx)dx ∫sinx sin^2⁡(cosx)dx

Here is the technique to solve these 4 integrals by integration by substitution ∫ cosx cos^2⁡ (sinx) dx ∫ sinx cos^2⁡ (cosx) dx ∫ cosx sin^2⁡ (sinx) dx ∫ sinx sin^2⁡ (cosx) dx #CalculusHelp #Integral #Integrations #IntegrationbySubstitution #Substitution
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Calculus Help: Integral ∫ sin2x/e^x dx - Integration by parts - Techniques
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Calculus Help: Integral ∫ sin2x/e^x dx - Integration by parts - Techniques

Calculus Help: Integral ∫ sin2x/e^x dx - Integration by parts - Techniques #Integral #Integrations #Calculus #Formula #Parts
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Calculus Help: Integral ∫ 1/(3+2tanx) dx - Find the coefficient - Integration by substitution
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Calculus Help: Integral ∫ 1/(3+2tanx) dx - Find the coefficient - Integration by substitution

Calculus Help: Integral ∫ 1/(3+2tanx) dx - Find the coefficient - Integration by substitution #Integral #Integrations #Calculus #Antiderivative
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Calculus Help: Integral ∫ (x+1) e^2x e^(x^2 ) dx - Integration by substitution
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Calculus Help: Integral ∫ (x+1) e^2x e^(x^2 ) dx - Integration by substitution

Calculus Help: Integral ∫ (x+1) e^2x e^(x^2 ) dx - Integration by substitution #Calculus #Integral #Integrations #Substitution
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Calculus Help: Integral ∫ ∛(e^arccot⁡(4x) )/(16x^2+1) dx - Integration by substitution
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Calculus Help: Integral ∫ ∛(e^arccot⁡(4x) )/(16x^2+1) dx - Integration by substitution

∫▒〖∛(e^arccot⁡(4x) )/(16x^2+1) dx〗 Integration by substitution #Integration #Calculus #Substitution #Techniques
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Calculus Help: ∫ (2+(lnx)^2)/(x(2-lnx)) dx - Integration by substitution
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Calculus Help: ∫ (2+(lnx)^2)/(x(2-lnx)) dx - Integration by substitution

Here is the technique to solve this integration and how to find them in step-by-step #Integral #Integrations #Calculus #Substitution
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Calculus Help: Integral of ∫ arctanx / x^2 dx - Integration by parts and division
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Calculus Help: Integral of ∫ arctanx / x^2 dx - Integration by parts and division

Calculus Help: Integral of ∫ arctanx / x^2 dx - Integration by parts and division #Integral #Calculus #Parts
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Calculus Help: Integral ∫ 1/(x^3+x) dx - Integration by trigonometric substitution
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Calculus Help: Integral ∫ 1/(x^3+x) dx - Integration by trigonometric substitution

Calculus Help: Integral ∫ 1/(x^3+x) dx - Integration by trigonometric substitution #Integral #Integrations #Calculus #Techniques #TrigonometricSubstitution
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Calculus Help: Integral ∫ dx/(x^2 √(x^2-1)) - Integration by trigonometric substitution
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Calculus Help: Integral ∫ dx/(x^2 √(x^2-1)) - Integration by trigonometric substitution

Calculus Help: Integral ∫ dx/(x^2 √(x^2-1)) - Integration by trigonometric substitution #Integral #Integrations #Trigonometric #Techniques
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Calculus Help: Integral of dx/(x^3 √(x^2-1)) - Integration of trigonometric substitution
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Calculus Help: Integral of dx/(x^3 √(x^2-1)) - Integration of trigonometric substitution

Calculus Help: Integral of dx/(x^3 √(x^2-1)) - Integration of trigonometric substitution #Integral #Substitution #Trigonometric
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Calculus Help: Integral ∫ x^3/√(x^2+100) dx - Integration by trigonometric substitution
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Calculus Help: Integral ∫ x^3/√(x^2+100) dx - Integration by trigonometric substitution

Calculus Help: Integral ∫ x^3/√(x^2+100) dx - Integration by trigonometric substitution #Integral #Trigonometric #Substitution #Calculus
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Calculus Help: Integral ∫ dx/(x^2 √(x^2-9)) - Integration by trigonometric substitution
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Calculus Help: Integral ∫ dx/(x^2 √(x^2-9)) - Integration by trigonometric substitution

Calculus Help: Integral ∫ dx/(x^2 √(x^2-9)) - Integration by trigonometric substitution #Trigonometric #Substitution #Integrals #Calculus
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Calculus Help: Integral from 0 to 1 x^x dx - Gamma Function - Taylor Series - Substitution
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Calculus Help: Integral from 0 to 1 x^x dx - Gamma Function - Taylor Series - Substitution

Calculus Help: Integral from 0 to 1 x^x dx - Gamma Function - Taylor Series - Substitution Here is the technique to solve this question and how to find them in step-by-step #Techniques #Solutions #Answers #Formula #GammaFunctions #Substitution
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Calculus Help: ∫ √(1+x^2 )/x dx - Integration by trigonometric substitution - Techniques - SOLVED!
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Calculus Help: ∫ √(1+x^2 )/x dx - Integration by trigonometric substitution - Techniques - SOLVED!

Calculus Help: ∫ √(1+x^2 )/x dx - Integration by trigonometric substitution - Techniques - SOLVED! #TrigonometricSubstitution #Substitution #Calculus
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Calculus Help: Integral ∫ x sin⁡(x/a)dx - Integration by parts - Techniques
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Calculus Help: Integral ∫ x sin⁡(x/a)dx - Integration by parts - Techniques

Here is the technique to solve this integration and how to find them in step-by-step #Integral #Integrations #Parts #Calculus
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Calculus Help: Find the value of integral of x^2 lnx dx - Integration by parts
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Calculus Help: Find the value of integral of x^2 lnx dx - Integration by parts

Calculus Help: Find the value of integral of x^2 lnx dx - Integration by parts #Integral #Integration #Calculus #Parts
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Calculus Help: Improper Integrals - ∫ From 1 to ∞ 1/x^2 dx - Integration - Techniques
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Calculus Help: Improper Integrals - ∫ From 1 to ∞ 1/x^2 dx - Integration - Techniques

Calculus Help: Improper Integrals - ∫ From 1 to ∞ 1/x^2 dx - Integration - Techniques #ImproperIntegrals #Integrations #Calculus #Integral #Antiderivative
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Calculus Help: Integral ∫ (x^2-3x)/√(x+4) dx - Integration by substitution - Techniques
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Calculus Help: Integral ∫ (x^2-3x)/√(x+4) dx - Integration by substitution - Techniques

Calculus Help: Integral ∫ (x^2-3x)/√(x+4) dx - Integration by substitution - Techniques #Integrals #Integrations #Calculus #Antiderivative
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Calculus Help: Integral of ∫ dx/√(25-x^2 ) - Integration by trigonometric substitution
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Calculus Help: Integral of ∫ dx/√(25-x^2 ) - Integration by trigonometric substitution

Calculus Help: Integral of ∫ dx/√(25-x^2 ) - Integration by trigonometric substitution #Integral #TrigonometricSubstitution #Calculus
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Calculus Help: Integral: x e^(x^2) dx - Integration by substitution - Techniques - Solutions
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Calculus Help: Integral: x e^(x^2) dx - Integration by substitution - Techniques - Solutions

Calculus Help: Integral: x e^(x^2) dx - Integration by substitution - Techniques - Solutions #Integration #Calculus #Substitution
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Calculus Help: Integral of e^(x^2) - Imaginary Error Function
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Calculus Help: Integral of e^(x^2) - Imaginary Error Function

Calculus Help: Integral of e^(x^2) - Imaginary Error Function #Integral #ImaginaryErrorFunction #Calculus
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Calculus Help: Determine the area under the curve y^2=4x and y-2x+4=0 - Application of Integration
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Calculus Help: Determine the area under the curve y^2=4x and y-2x+4=0 - Application of Integration

Here is the technique to solve this integration and how to find them in here #Integral #Integration #Calculus #Formula #Techniques #Answers
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Calculus Help: Integral ∫ From 0 to 1 sinx tanx dx - Basic Trigonometry
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Calculus Help: Integral ∫ From 0 to 1 sinx tanx dx - Basic Trigonometry

Here is the technique to solve this question and how to find them in step-by-step #Integral #Integrations #Calculus #Formula
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Calculus Help: Integral of 1/(x^2 √(9-x^2 )) dx - Integration by Trigonometric Substitution
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Calculus Help: Integral of 1/(x^2 √(9-x^2 )) dx - Integration by Trigonometric Substitution

Calculus Help: Integral of 1/(x^2 √(9-x^2 )) dx - Integration by Trigonometric Substitution #Integration #Integrals #Trigonometric #Substitution #Calculus
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Calculus Help: ∫_0^1 arcsinx dx Integration by parts and substitution
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Calculus Help: ∫_0^1 arcsinx dx Integration by parts and substitution

Here is the technique to solve this integration and how to find it ∫_0^1▒arcsinx dx Integration by parts #Integral #Integrations #Calculus #Substitution
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Calculus Help: Integral ∫ 0^2 x√(3x^2+5) dx - Integration by substitution
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Calculus Help: Integral ∫ 0^2 x√(3x^2+5) dx - Integration by substitution

Here is the technique to solve this question and how to find them in step-by-step #Calculus #Integral #Integrations
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Calculus Help: Find the arc length y=4/3 x^(3/2) on the interval [0,1]
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Calculus Help: Find the arc length y=4/3 x^(3/2) on the interval [0,1]

Here is the technique to solve the question and find the arc length #ArcLength #Calculus #Formula
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Calculus Help: Find the area between the curve y=x^2 and y=-x^2 + 18x
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Calculus Help: Find the area between the curve y=x^2 and y=-x^2 + 18x

Calculus Help: Find the area between the curve y=x^2 and y=-x^2 + 18x #Calculus #Integral #Integrations #Area
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Calculus Help: ∫ 1/√(1+9x^2 ) dx - Integration by trigonometric substitution - Step-by-step
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Calculus Help: ∫ 1/√(1+9x^2 ) dx - Integration by trigonometric substitution - Step-by-step

Here is the technique to solve this integration and how to find them in step-by-step #Integral #Integration #Calculus #Formula
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Calculus Help: Integral of x^2 sinx dx - Integration by parts by using the table
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Calculus Help: Integral of x^2 sinx dx - Integration by parts by using the table

Calculus Help: Integral of x^2 sinx dx - Integration by parts by using the table #Integral #Integrations #Calculus #Parts #IntegrationByParts
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Calculus Help: Use cylindrical shells to find the volume of the solid generated when: y=x^2 1 to 6
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Calculus Help: Use cylindrical shells to find the volume of the solid generated when: y=x^2 1 to 6

Calculus Help: Use cylindrical shells to find the volume of the solid generated when: y=x^2 1 to 6 #Integral #Integrations #Calculus #Techniques
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If the function f(x) has continuous derivative, 2f(x)+3f(1-x)=√(1-x^2 ) then ∫_0^1 f'(x) dx
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If the function f(x) has continuous derivative, 2f(x)+3f(1-x)=√(1-x^2 ) then ∫_0^1 f'(x) dx

If the function f(x) has continuous derivative on [0;1] and satisfies the condition 2f(x)+3f(1-x)=√(1-x^2 ) then calculate ∫_0^1 f'(x) dx A.I=0 B.I=1 C.I=1/2 D.I=3/2 #CalculusHelp #Integral #Integrations #Solutions
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Find the approximation of c such that ∫ from c to x f(t) dt = x^3 + 3x^2 + 2x - 3
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Find the approximation of c such that ∫ from c to x f(t) dt = x^3 + 3x^2 + 2x - 3

#Integral #Integrations #Antiderivative
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Calculus Help: ∫ dx/(x^2 √(a^2-x^2 )) - Integration by trigonometric substitution
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Calculus Help: ∫ dx/(x^2 √(a^2-x^2 )) - Integration by trigonometric substitution

Calculus Help: ∫ dx/(x^2 √(a^2-x^2 )) - Integration by trigonometric substitution #CalculusHelp #Integrals #Integrations #TrigonometricSubstitution #Substitution
41
Calculus Help: Integral ∫ tanx/tan2x dx - Integration by basic trigonometry - Techniques
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Calculus Help: Integral ∫ tanx/tan2x dx - Integration by basic trigonometry - Techniques

Here is the technique to solve Integral tanx/tan2x dx - Integration by basic trigonometry - Techniques #Integral #Integrations #Calculus #Techniques
42
Calculus Help: Integral ∫ cos^2 ⁡x dx and ∫ sin^2 ⁡x dx - Integration by Trigonometric identities
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Calculus Help: Integral ∫ cos^2 ⁡x dx and ∫ sin^2 ⁡x dx - Integration by Trigonometric identities

Here is the technique to solve this question and how to find the question #Calculus #Integrals #Integrations #Solutions #TrigonometricSubstitution
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Calculus Help: Application of Parabola and Integration (Arc Length) - Ballistic Missile - Red Alert
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Calculus Help: Application of Parabola and Integration (Arc Length) - Ballistic Missile - Red Alert

Here is the technique to solve this question related to the parabolic projectile and find the distance of the ballistic missile after reaching the target. #Calculus #BallisticMissile #Missile #ArcLength #Techniques #Solutions #Formula
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Calculus Help: Integral of dx/√(1+x^2 ) - Integration by trigonometric substitution
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Calculus Help: Integral of dx/√(1+x^2 ) - Integration by trigonometric substitution

Here is the technique to trigonometric substitution and how to solve it #Integral #integration #Technique #Calculus #Formula #Solution #Technique #Answer
45
Calculus Help: Integral ∫ x √(x^2+4) dx - Integration by substitution - 置換積分
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Calculus Help: Integral ∫ x √(x^2+4) dx - Integration by substitution - 置換積分

Here is the technique to solve this integration and how to find them in step-by-step #Integral #Integrations #Solutions #Calculus
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Calculus Help: ∫ x/√(x^2+4) dx - Integration by substitution
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Calculus Help: ∫ x/√(x^2+4) dx - Integration by substitution

Here is the technique to solve this integration and how to find them in step-by-step #Integral #Integrations #Calculus #Formula
47
Calculus Help: Integral ∫ √(1-x^2 )/x^4 dx - Integration by trigonometric substitution
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Calculus Help: Integral ∫ √(1-x^2 )/x^4 dx - Integration by trigonometric substitution

Calculus Help: Integral ∫ √(1-x^2 )/x^4 dx - Integration by trigonometric substitution #Integral #Integrations #Substitution #TrigonometricSubstitution
48
Calculus Help: ∫ ∛x/(∛x+1) dx, ∫ 1/(1+√3x) dx - Integration by substitution - Techniques
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Calculus Help: ∫ ∛x/(∛x+1) dx, ∫ 1/(1+√3x) dx - Integration by substitution - Techniques

Here is the technique to solve these 2 integrals and how to find them in step-by-step #Calculus #Integrals #Integrations #substitution #integrationbysubstitution
49
Calculus Help: Basic Integral ∫ √(3x-10) dx - Integration - Techniques
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Calculus Help: Basic Integral ∫ √(3x-10) dx - Integration - Techniques

Here is the technique to solve this integration and how to find them #Integrals #Integrations #Calculus #Basic Transcript
50
Calculus Help: Integral of lnx/x^2 dx - Integration by parts - Techniques
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Calculus Help: Integral of lnx/x^2 dx - Integration by parts - Techniques

Here is the technique to solve this question and how to find them in step-by-step #Integral #Integrations #Calculus #Formula
51
Calculus Help: Integral ∫ x sin⁡(3x) dx - Integration by parts - Techniques - Solutions
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Calculus Help: Integral ∫ x sin⁡(3x) dx - Integration by parts - Techniques - Solutions

Here is the technique to solve this integration by parts and how to find them in step-by-step #Integrals #Integrations #Calculus #Formula
52
Calculus Help: Integral of ∫ e^ax cos⁡(bx)dx - Integration by parts and techniques
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Calculus Help: Integral of ∫ e^ax cos⁡(bx)dx - Integration by parts and techniques

Here is the technique to solve this integral and how to find them in step-by-step #Integrals #Integrations #IntegrationByParts #Calculus #Formula
53
Calculus Help: Integral ∫ x^2 cos⁡(2x) dx - Integration by parts - Techniques - SOLVED!!!
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Calculus Help: Integral ∫ x^2 cos⁡(2x) dx - Integration by parts - Techniques - SOLVED!!!

Here is the technique to solve the question and how to find by integration by parts #Integrals #Integration #Calculus #Formula #Techniques #IntegrationByParts
54
Calculus Help: Integral ∫ xe^(1/2 x) dx - Integration by parts - Techniques
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Calculus Help: Integral ∫ xe^(1/2 x) dx - Integration by parts - Techniques

Here is the technique to solve the question and integration by parts #IntegrationByParts #Techniques #Solutions #Calculus #Integrals #Integrations
55
Integral ∫ From 2 to 4 √(ln⁡(9-x) )/(√(ln⁡(9-x) )+√(ln⁡(3+x))) dx - Integration by substitution
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Integral ∫ From 2 to 4 √(ln⁡(9-x) )/(√(ln⁡(9-x) )+√(ln⁡(3+x))) dx - Integration by substitution

Here is the technique to solve this question and how to find them in step-by-step #Techniques #Calculus #Formula #Substitution #Integrals #Integrations
56
Calculus Help: Find the limits - lim (x→0) (1-cosx)/sin2x - Techniques - SOLVED!!!
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Calculus Help: Find the limits - lim (x→0) (1-cosx)/sin2x - Techniques - SOLVED!!!

Here is the technique to solve this limit and how to find them in step-by-step #Limits #Functions #Calculus
57
Calculus Help: Integral ∫ cot^3⁡ x csc^4 ⁡x dx - Integration with Substitution - trigonometry
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Calculus Help: Integral ∫ cot^3⁡ x csc^4 ⁡x dx - Integration with Substitution - trigonometry

Here is the technique to solve this integration and how to find them in step-by-step #Integral #Integrations #Calculus #Trigonometry #Antiderivative
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Calculus Help: Integral of ∫ cot^5⁡ x dx - Integration by substitution - Trigonometry
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Calculus Help: Integral of ∫ cot^5⁡ x dx - Integration by substitution - Trigonometry

Here is the technique to solve this integration and how to find them in step-by-step #Integral #Integrations #Calculus #Formula #Solutions
59
Calculus Help: Integral ∫ tan^6 ⁡x sec^4⁡ x dx - Integration by substitution - Trigonometry
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Calculus Help: Integral ∫ tan^6 ⁡x sec^4⁡ x dx - Integration by substitution - Trigonometry

Here is the technique to solve the integration and how to find #Integral #Antiderivative #Integrations #Calculus #Trigonometry
60
Calculus Help: Integral of ∫ tan^6⁡ x dx - Integration by substitution - Trigonometry
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Calculus Help: Integral of ∫ tan^6⁡ x dx - Integration by substitution - Trigonometry

Here is the technique to solve this integration and how to find them in step-by-step #Integral #Integrations #Calculus #Formula
61
Polar Coordinates: Evaluate the volume of the cylinder x^2+z^2=9, bounded by the planes
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Polar Coordinates: Evaluate the volume of the cylinder x^2+z^2=9, bounded by the planes

Evaluate the volume of the cylinder x^2+z^2=9, bounded by the planes x=0, y=0, z=0 and x+2y=2 on first octant Here is the technique to solve the question related to polar coordinates and how to find them in step-by-step #Calculus #Techniques #PolarCoordinates #TripleIntegrals
62
Calculus Help: Integral ∫ sin⁡(2-6x) dx - Basic Integration
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Calculus Help: Integral ∫ sin⁡(2-6x) dx - Basic Integration

Here is the technique to solve this question and how to find them in step-by-step #Integral #Integrations #Solutions #Answered
63
Calculus Help: Integral of sin^3⁡ x cosx dx - Integration by substitution
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Calculus Help: Integral of sin^3⁡ x cosx dx - Integration by substitution

Here is the technique to solve this integration and how to find them in step-by-step #Integral #Integration #Calculus #Substitution
64
Calculus Help: ∫ √(16-9x^2 ) dx - Integration by trigonometric substitution
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Calculus Help: ∫ √(16-9x^2 ) dx - Integration by trigonometric substitution

Here is the technique to solve this integration and how to find them in step-by-step #Integral #Integrations #Calculus #Formula #TrigonometricSubstitution
65
Integration by Substitution: ∫ (7x+4)^5 dx, ∫ e^x/(2e^x+3)^7 dx, ∫ (x^2+2x)/(x^3+3x^2-4) dx
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Integration by Substitution: ∫ (7x+4)^5 dx, ∫ e^x/(2e^x+3)^7 dx, ∫ (x^2+2x)/(x^3+3x^2-4) dx

∫ (7x+4)^5 dx, ∫ e^x/(2e^x+3)^7 dx, ∫ (x^2+2x)/(x^3+3x^2-4) dx Here is the technique to solve these integrations and how to find them in step-by-step #Integrals #Integrations #Antiderivative #Solutions #Substitution #IntegrationBySubstitution
66
Introduction of Integration: Calculus - ∫ (x^2+1/(2x)^3 )dx ∫ (7x^4+8x^3+9^x )dx
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Introduction of Integration: Calculus - ∫ (x^2+1/(2x)^3 )dx ∫ (7x^4+8x^3+9^x )dx

∫ (x^2+1/(2x)^3 )dx ∫ (7x^4+8x^3+9^x )dx ∫ (3 csc^2⁡x-5secx tanx) dx #Calculus #Integrals #Integrations #Introduction
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The Hardest High School Math by Trigonometric Substitution in Vietnam - Integral with long series
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The Hardest High School Math by Trigonometric Substitution in Vietnam - Integral with long series

Here is the technique to solve the integral Integral ( 1 + tan^2 x)(1 + tan^3 x)...(1 + tan^2020 x) + ... + (1+tanx)(1 + tan^2 x)... (1 + tan^2019 x) / (1 + tanx)(1 + tan^2 x)(1 + tan^3 x) ... (1+tan^2020 x) dx #Integral #Integrations #Calculus #TheHardestHighSchoolMath #TrigometricSubstitution
68
Integral: 3 sin⁡(2x) ; 5 sin⁡(3x) cos^3⁡ (3x) ; e^2x/(e^2x+3) ; x√(x+3) ; (x)/∛(x+1) ∫1/(x√(7-x^2 ))
10:13

Integral: 3 sin⁡(2x) ; 5 sin⁡(3x) cos^3⁡ (3x) ; e^2x/(e^2x+3) ; x√(x+3) ; (x)/∛(x+1) ∫1/(x√(7-x^2 ))

Here is the technique to solve these integrations and how to find them in step-by-step #Integrals #Integrations #Calculus
69
Calculus Techniques: Integration ∫ 1 dx/(1+tanx) - Integration by substitution - SOLVED!!
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Calculus Techniques: Integration ∫ 1 dx/(1+tanx) - Integration by substitution - SOLVED!!

Here is the technique to solve this integration and how to find them #Integral #Integration #Calculus #Formula #Techniques
70
Integral Help: ∫ √(1+x^2 )/x dx - Integration by trigonometric substitution - Solutions
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Integral Help: ∫ √(1+x^2 )/x dx - Integration by trigonometric substitution - Solutions

Here is the technique to solve this integration and how to find them in step-by-step #Integral #Integrations #Solutions
71
Calculus Help: Integral from 4 to 7 - dx/(x^2-5x+6) - Techniques - Partial Fractions
3:18

Calculus Help: Integral from 4 to 7 - dx/(x^2-5x+6) - Techniques - Partial Fractions

Here is the technique to solve this question and how to find them in step-by-step #PartialFractions #Integrations #Integrals #Calculus
72
Integral Help: ∫ Integration from 5 to 10 x^2 lnx dx - Integration by parts - Techniques in Cal
2:10

Integral Help: ∫ Integration from 5 to 10 x^2 lnx dx - Integration by parts - Techniques in Cal

Here is the full video to show how to solve the integration and how to find them in step-by-step #Integrals #Integrations #Parts #Answered
73
Calculus Help: Integration from 4 to 9 √x/(√x-1) dx - Techniques - Integration by substitution
3:25

Calculus Help: Integration from 4 to 9 √x/(√x-1) dx - Techniques - Integration by substitution

Here is the full video to solve this question and how to find them in step-by-step #Integrals #Integrations #Solutions #Calculus
74
Calculus Help: Find the Integral of (2x^2+4x-3)/x^2 dx - Techniques - Solutions
2:52

Calculus Help: Find the Integral of (2x^2+4x-3)/x^2 dx - Techniques - Solutions

Here is the technique to solve this integration and how to find them in step-by-step #Techniques #Solutions #Answered
75
Calculus Help: Integral of (x+1)dx/(x^3+x^2-6x) - Integration by partial fractions
4:52

Calculus Help: Integral of (x+1)dx/(x^3+x^2-6x) - Integration by partial fractions

Here is the technique to solve this integration and how to find them in step-by-step #Techniques #Solutions #Answered #PartialFractions
76
Calculus Help: Integrals: A solid lies between planes perpendicular to the x-axis at x = 0 and x=9
3:14

Calculus Help: Integrals: A solid lies between planes perpendicular to the x-axis at x = 0 and x=9

Full question: A solid lies between planes perpendicular to the x-axis at x = 0 and x=9. The cross sections perpendicular to the x-axis between these planes are squares whose bases run from the parabola y = - 4√x to the parabola y = 4√x. Find the volume of the solid #CalculusHelp #CrossSection #Integral
77
Calculus Help: Integral ∫ x^3/(4x^2+9)^(3/2) dx - Integration by substitution - Techniques
3:53

Calculus Help: Integral ∫ x^3/(4x^2+9)^(3/2) dx - Integration by substitution - Techniques

Here is the technique to solve this integration and how to find them in step-by-step #Integral #Integration #Solutions #Answered #Substitution
78
Integral: ∫ dx/(e^x - 1) and how to solve - Integration - Step-by-step
3:19

Integral: ∫ dx/(e^x - 1) and how to solve - Integration - Step-by-step

Here is the technique to solve this integration and how to find them in step-by-step #Integral #Integration #Step-by-step #Calculus
79
Calculus Help: Triple Integrals - ∫ From 0 to 1 ∫ From 0 to 1 ∫ From 0 to 1 e^(x+y+z) dx dy dz
2:22

Calculus Help: Triple Integrals - ∫ From 0 to 1 ∫ From 0 to 1 ∫ From 0 to 1 e^(x+y+z) dx dy dz

Here is the technique to solve this question and how to find them in step-by-step #Techniques #Integrals #Integrations #TripleIntegrals
80
Calculus Help: ∫ x^3 sinx dx - Integration by parts - Techniques - Solutions
4:09

Calculus Help: ∫ x^3 sinx dx - Integration by parts - Techniques - Solutions

Here is the technique to solve this integration and how to find them in here by integration by parts #Integral #Integration #Calculus #Formula #Solutions
81
Calculus Help: Integral of ∫ arctan⁡(3x)dx - Integration by parts and how to solve
3:20

Calculus Help: Integral of ∫ arctan⁡(3x)dx - Integration by parts and how to solve

Here is the technique to solve this question and how to find them in step-by-step #Integral #Integrations #Solutions #Answered
82
Calculus Help: sin^2 x dx / sqrt(1-cosx) - sin^2 x dx/ √(1 - cosx) - Integration by substitution
4:30

Calculus Help: sin^2 x dx / sqrt(1-cosx) - sin^2 x dx/ √(1 - cosx) - Integration by substitution

Here is the technique to solve this integration and how to find them in step-by-step #Techniques #Solutions #Integrals #Integration
83
Calculus Help: Integral ∫ (2x^2-x+4)/(x^3+4x) dx - Integration by division - Techniques
5:39

Calculus Help: Integral ∫ (2x^2-x+4)/(x^3+4x) dx - Integration by division - Techniques

Here is the technique to solve this question and how to find them in step-by-step #Calculus #Solutions #Techniques #Division #Integrations
84
Calculus Help: ∫ sin^4 ⁡x cos^6⁡ x dx - Integration with trigonometry - Equation - Integrals
8:04

Calculus Help: ∫ sin^4 ⁡x cos^6⁡ x dx - Integration with trigonometry - Equation - Integrals

Here is the technique to solve this integration and how to find them in step-by-step #Techniques #Solutions #Answered
85
Calculus Help: Integral of cos^3⁡x/(1-sinx) dx - Integration by substitution - Trigonometry
1:44

Calculus Help: Integral of cos^3⁡x/(1-sinx) dx - Integration by substitution - Trigonometry

Here is the technique to solve this integration and how to find them in step-by-step #Techniques #Calculus #Solutions #Substitution
86
Calculus Help: Separable Differential Equation: dy/dx=e^(x-y) - Exponent and Power Equation
1:55

Calculus Help: Separable Differential Equation: dy/dx=e^(x-y) - Exponent and Power Equation

Here is the technique to solve the question and how to find this separable differential equation #DiffernetialEquations #Calculus #SeparableDifferentialEquations #Exponent
87
Calculus Help: Integral ∫ sinx √(1+cosx)dx - Integration by substitution - Techniques
2:15

Calculus Help: Integral ∫ sinx √(1+cosx)dx - Integration by substitution - Techniques

Here is the technique to solve this integration and how to find them in step-by-step #Techniques #Calculus #Integrations #Integrals #Solutions
88
Calculus Help: Integral of ∫sin4x cos4x dx (Two ways) - Trigonometry Identities and Substitution
2:55

Calculus Help: Integral of ∫sin4x cos4x dx (Two ways) - Trigonometry Identities and Substitution

Here is the technique to solve this integration and how to solve it #Integral #Integration #Calculus #Formula
89
Calculus Help: Integral ∫ x^2/√(9-25x^2 ) dx - Integration by trigonometric substitution
4:51

Calculus Help: Integral ∫ x^2/√(9-25x^2 ) dx - Integration by trigonometric substitution

Here is the technique to solve this question and how to find them in step-by-step #Techniques #Calculus #Integrals #Integrations #Solutions
90
Calculus Help: Integral dx/(x√(x^2-4)) - Integration by substitution dx/(x sqrt(x^2-4)) Square root
6:17

Calculus Help: Integral dx/(x√(x^2-4)) - Integration by substitution dx/(x sqrt(x^2-4)) Square root

Here is the technique to solve integration and how to find them in step-by-step #Integral #Integrations #Solutions
91
Calculus Help: Integral of dx/√(3-2x-x^2 ) - Integration by Trigonometric Substitution
5:26

Calculus Help: Integral of dx/√(3-2x-x^2 ) - Integration by Trigonometric Substitution

Here is a technique to answer the integral of dx/√(3-2x-x^2 ) #Integrals #integrations #Formula #Calculus
92
Calculus Help: Integral of ∫ cscx cotx dx - Integration by substitution
1:35

Calculus Help: Integral of ∫ cscx cotx dx - Integration by substitution

Here is the technique to solve this question and how to find the integral #Techniques #Solutions #Answered
93
Calculus Help: Find the exact length of the curve y=ln⁡(1-x^2 ),0≤x≤1/8 - Arc Length - Integration
5:10

Calculus Help: Find the exact length of the curve y=ln⁡(1-x^2 ),0≤x≤1/8 - Arc Length - Integration

Here is the technique to solve this question and how to find it in step-by-step:
94
Calculus Help: Integration x^3 ( 2+x^4)^5 dx , (x+1) √(2x+x^2) dx, 1/(1-6x)^4 dx
5:41

Calculus Help: Integration x^3 ( 2+x^4)^5 dx , (x+1) √(2x+x^2) dx, 1/(1-6x)^4 dx

Here is the technique to solve all 3 integrations and how to find them in step-by-step Integration x^3 ( 2+x^4)^5 dx , (x+1) √(2x+x^2) dx, 1/(1-6x)^4 dx
95
Calculus Help: Integral ∫ x^2 cos2x dx - Integration by parts - Techniques - Solutions
2:55

Calculus Help: Integral ∫ x^2 cos2x dx - Integration by parts - Techniques - Solutions

Here is the technique to solve about the integrals and how to find them in step-by-step ∫ x^2 cos2x dx
96
Calculus Help: Integral of sin^4 ⁡3x cos^2⁡ 3x dx - Integration by trigonometric identitity
4:45

Calculus Help: Integral of sin^4 ⁡3x cos^2⁡ 3x dx - Integration by trigonometric identitity

Here is the technique to solve this integral and how to find them in step-by-step: Integral of sin^4 ⁡3x cos^2⁡ 3x dx
97
Calculus Help: Volume bounded by y=1+secx and y=3 revolve about y=1
3:01

Calculus Help: Volume bounded by y=1+secx and y=3 revolve about y=1

Here is the technique to find this integration and how to solve about that #Integral #Integration #Calculus #Formula
98
Calculus Help: Double Integrals: e^(x+y) dydx - Basic Integration
1:47

Calculus Help: Double Integrals: e^(x+y) dydx - Basic Integration

Here is the technique to solve this double integral and how to find them in step-by-step
99
Calculus Help: Integral of (x-4)/(x^2-5x+6) dx - Integration by partial Fractions
3:00

Calculus Help: Integral of (x-4)/(x^2-5x+6) dx - Integration by partial Fractions

Here is the technique to solve this integration and how to solve about that #Integral #Integration #PartialFractions #Fractions
100
Double Integrals: Find ∫∫R y/x dA,where R is the region in the first quadrant x^2+y^2=1 ; x^2+y^2=4
8:04

Double Integrals: Find ∫∫R y/x dA,where R is the region in the first quadrant x^2+y^2=1 ; x^2+y^2=4

Here is the technique to find this double integrals by polar coordinates: Full question: Find ∫∫R y/x dA , where R is the region in the first quadrant lying between the circles x^2+y^2=1 and x^2+y^2=4 and between the lines y=0 and y=x #Calculus #DoubleIntegrals #Intgerations
101
Calculus Help: Integral of csc^4 x dx - Integration by trigonometric functions
1:31

Calculus Help: Integral of csc^4 x dx - Integration by trigonometric functions

Here is the technique to solve this integration and how to find them in step-by-step #Techniques #Solutions #Answered #Integrals
102
Calculus Help: Integral of sin2x cos4x dx - Integration by trigonometric substitution
1:24

Calculus Help: Integral of sin2x cos4x dx - Integration by trigonometric substitution

Here is the technique to solve this question and how to find them in step-by-step #Trigonometry #Trigonometric #Techniques #Calculus
103
Calculus Help: Integral ∫ (x^2+2x-1)/(2x^3+3x^2-2x) dx - Integration by partial fractions Technique
5:29

Calculus Help: Integral ∫ (x^2+2x-1)/(2x^3+3x^2-2x) dx - Integration by partial fractions Technique

Here is the technique to find the integral and how to solve them in here. Calculus Help: Integral ∫ (x^2+2x-1)/(2x^3+3x^2-2x) dx - Integration by partial fractions Technique
104
Calculus Help: Integral of dx/(a^2+x^2 )^(3/2) - Integration by trigonometric substitution
4:03

Calculus Help: Integral of dx/(a^2+x^2 )^(3/2) - Integration by trigonometric substitution

Here is the technique to answer this integration by trigonometry #Trigonometric #Trigonometry #Calculus #Formula #Solution
105
Calculus Help:Integral of arcsin⁡(4x)dx -Inverse Trigonometry and Integration by parts/ substitution
6:35

Calculus Help:Integral of arcsin⁡(4x)dx -Inverse Trigonometry and Integration by parts/ substitution

Here is the technique to solve this integral and how to find them in step-by-step
106
Calculus Help: Integral of dx/(x√(4x^2-9)) - How to solve this one?
5:35

Calculus Help: Integral of dx/(x√(4x^2-9)) - How to solve this one?

Here is the technique to solve the question and how to find them in step-by-step for this integration
107
Calculus Help: Integral ∫ x e^( ax ) dx - Integration by parts - 部分積分
1:33

Calculus Help: Integral ∫ x e^( ax ) dx - Integration by parts - 部分積分

Here is the technique to solve this question and how to find them in step-by-step
108
Calculus Help: ∫ e^(2x) cos⁡(3x) dx - Integration by parts - Techniques
4:04

Calculus Help: ∫ e^(2x) cos⁡(3x) dx - Integration by parts - Techniques

Here is the technique to solve this integral and how to find them in step-by-step: Calculus Help: ∫ e^(2x) cos⁡(3x) dx - Integration by parts - Techniques Here is the techniques to solve this integration and how to find them in here #Integral #Integration #Parts #Techniques
109
Calculus help: Integral of sec2x tan2x dx - Integration by substitution
2:10

Calculus help: Integral of sec2x tan2x dx - Integration by substitution

Here is the technique to solve this question and how to find them in step-by-step and how to find it
110
Calculus Help: Integral of e^2x sin3x dx - Integration by parts
3:14

Calculus Help: Integral of e^2x sin3x dx - Integration by parts

Here is the technique to solve this question and how to find them in step-by-step: Calculus Help: Integral of e^2x sin3x dx - Integration by parts
111
Calculus Help: Integral ∫ tan^2 ⁡x sec^3 ⁡x dx - Integration with trigonometry - Techniques
8:52

Calculus Help: Integral ∫ tan^2 ⁡x sec^3 ⁡x dx - Integration with trigonometry - Techniques

Here is the technique to solve this question and how to find them in here #Trigonometry #Techniques #Solutions #Calculus
112
Calculus Help: Integral of e^2x sinx dx - Integration by parts - Techniques
3:20

Calculus Help: Integral of e^2x sinx dx - Integration by parts - Techniques

Here is the technique to find this integration and how to find them with step-by-step #Parts #IntegrationbyParts #Integral #Integration #Calculus
113
Calculus Help: Integral of x^2 e^3x dx - Integration by Substitution - High School Math - SOLVED!!!
4:14

Calculus Help: Integral of x^2 e^3x dx - Integration by Substitution - High School Math - SOLVED!!!

Here is the technique to answer the Integral of x^2 e^3x dx #Integrals #Integration #Technique #Answer #Solution #Calculus
114
Calculus Help: Integral from 0 to infinity e^(-x^2) dx with Gamma Function
3:47

Calculus Help: Integral from 0 to infinity e^(-x^2) dx with Gamma Function

Here is the video to illustrate about the integral from 0 to infinity e^(-x^2) dx #Integral #Calculus #Formula #Gamma #GammaFunction
115
Calculus Help: Lim {x approaches to 0} (tanx / x)^(1/x) - L'Hospital - Exponential Functions
8:36

Calculus Help: Lim {x approaches to 0} (tanx / x)^(1/x) - L'Hospital - Exponential Functions

Here is the technique to find this limit and how to answer it #Limit #Techniques #Calculus #Formula
116
Calculus Help: Integral ∫ (3x+5)/(x^3-x^2-x+1) dx - Integration by partial fractions - Techniques
4:44

Calculus Help: Integral ∫ (3x+5)/(x^3-x^2-x+1) dx - Integration by partial fractions - Techniques

Calculus Help: Integral ∫ (3x+5)/(x^3-x^2-x+1) dx - Integration by partial fractions - Techniques Here is the technique to solve this integration and how to solve them in here #Integral #Integration #Calculus #Formula
117
Calculus Help: If f(x) is continuous and ∫f(x)dx=4 Find ∫ xf(x^2 ) dx - Integration techniques
2:12

Calculus Help: If f(x) is continuous and ∫f(x)dx=4 Find ∫ xf(x^2 ) dx - Integration techniques

Here is the technique to solve this integration and how to find them #Integral #Integration #Calculus
118
Calculus Help: Integral of x tanx - Integration by parts
4:05

Calculus Help: Integral of x tanx - Integration by parts

Here is the technique to find the integration #Integral #Integration #Calculus #Formula
119
Evaluate the double integral ∫∫D 10xy dA,where D is the triangular region vertices (0,0),(1,2),(0,3)
8:03

Evaluate the double integral ∫∫D 10xy dA,where D is the triangular region vertices (0,0),(1,2),(0,3)

Here is the technique to solve this double integral and how to find them #DoubleIntegrals #Calculus #Formula
120
Calculus Help: Integral of ∫ x^2/√(16-x^2 ) dx - Integration by trigonometric substitution - SOLVED!
4:39

Calculus Help: Integral of ∫ x^2/√(16-x^2 ) dx - Integration by trigonometric substitution - SOLVED!

Find the integral of ∫▒〖x^2/√(16-x^2 ) dx〗 #Calculus #Help #Integral #Integration #Substitution
121
Calculus Help: Integral of sin^2 x cos^4 x dx - Integration by trigonometric function
6:29

Calculus Help: Integral of sin^2 x cos^4 x dx - Integration by trigonometric function

Here is the video to illustrate how to find the integration by trigonometric function #Trigonometric #Function #Calculus

Calculus Help: An object of mass m is dropped into the sea at the surface. It is subject to a

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Health & Science CalculusHelp Integrals differentialequations PartialFractions

An object of mass m is dropped into the sea at the surface. It is subject to a constant gravitational acceleration g and water resistance. (a) (4 points) If the water resistance is proportional to the object's velocity v(t) with coefficient b ≫ 0, so that Newton's second law gives b dv/dt =g- b/m v show that the object's velocity as a function of time t is given by v(t) = mg/b (1-e^(-bt/m)). We take downward to be the positive direction and the object is at rest when it is dropped at t=0. (b) (4 points) If instead the water resistance is quadratic in the velocity, so that Newton's second law gives dv/dt =g- b/m v^2 dt m dv dt find the object's velocity as a function of time t, again assuming that the object is dropped from rest. [Hint: Write Newtons' law as = g(1 − k^2v^2) where k = √b/mg. Then the algebra is a little less messy. After obtaining the final answer in terms of k, remember to replace k by √b/mg.] (c) (2 points) If the object could fall forever under these conditions without hitting the bottom, show that as t→ ∞ the velocity in part (a) approaches terminal velocity v → mg/b. What terminal velocity does the velocity in part (b) approach?

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#differentialequations
#PartialFractions

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