   Chapter 5.2, Problem 12E ### 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  - 1 ) 3 ( 2 x )   d x

To determine

To calculate: The value of the provided indefinite integral (x21)3(2x)dx.

Explanation

Given Information:

The provided indefinite integral is (x21)3(2x)dx.

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=(x21)3(2x)dx

Let

x21=u … (1)

Differentiate the above equation with respect to x;

ddx(x21)=dudxddx(x2)ddx(1)=dudx(2x)=dudx

Or

(2x)dx=du … (2)

Substitute the values of x21 and (2x)dx from equations (1) and (2) respectively in the provided integral;

I=

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