   Chapter 5, Problem 25RE ### 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 21–32, find the indefinite integral. Check your result by differentiating. ∫ ( x 2 + 8 x ) 2 ( x + 4 ) d x

To determine

To calculate: The indefinite integral (x2+8x)2(x+4)dx.

Explanation

Given Information:

The provided indefinite integral is (x2+8x)2(x+4)dx.

Formula used:

The power rule of integrals:

undu=un+1n+1+C (n1)

The power rule of differentiation:

ddxun=nun1+C

Calculation:

Consider the indefinite integral:

(x2+8x)2(x+4)dx

Let u=x2+8x, then derivative will be,

du=d(x2+8x)=(2x+8)dx

Rewrite integration as,

(x2+8x)2(x+4)dx=12(x2+8x)2(2x+8)dx

Substitute du for (2x+8)dx and u for x2+8x in provided integration

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