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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Checkpoint 2 Worked-out solution available at LarsonAppliedCalculus.com

Find x 3 ( 3 x 4   +   1 ) 2   d x .

To determine

To calculate: The value of the provided indefinite integral x3(3x4+1)2dx.

Explanation

Given Information:

The provided indefinite integral is x3(3x4+1)2dx.

Formula Used:

According to the general power rule for integration,

If u is a differentiable function of x, then

undu=un+1n+1+C,

where n1

Calculation:

Consider the indefinite integral say I,

I=x3(3x4+1)2dx

Multiply and divide by 12 in the right-hand side of above integral,

I=11212x3(3x4+1)2dx

Take the factor 112 out of the integrand,

I=11212x3(3x4+1)2dx

Let

3x4+1=u …… (1)

Differentiate the above equation with respect to x,

ddx(3x4+1)=dudxddx(

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