   Chapter 5.2, Problem 19E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Applying the General Power Rule In Exercises 9-34, find the indefinite integral. Check your result by differentiating. See Examples 1, 2, 3, and 5. ∫ x 2 ( 2 x 3   -   1 ) 4   d x

To determine

To calculate: The value of the provided indefinite integral x2(2x31)4dx.

Explanation

Given Information:

The provided indefinite integral is x2(2x31)4dx.

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=x2(2x31)4dx

Multiply and divide by 6 in the right-hand side of above integral;

I=166x2(2x31)4dx

Take the factor 16 out of the integrand;

I=166x2(2x31)4dx

Let

2x31=u … (1)

Differentiate the above equation with respect to x;

ddx(2x31)=dudxddx(2x3)ddx(1)=dudx6x2=dudx

Or

6x2dx=du … (2)

Substitute the values of 2

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