   Chapter 5.3, Problem 6QY ### 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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# In Exercises 1-9, find the indefinite integral. Check your result by differentiating. ∫ x ( 5 x 2 − 2 ) 4 d x

To determine

To calculate: The indefinite integral x(5x22)4dx.

Explanation

Given Information:

The provided indefinite integral is x(5x22)4dx

Formula used:

The power rule of integrals:

undu=xn+1n+1+C (for n1)

The power rule of differentiation:

dduun=nun1+C

Calculation:

Consider the indefinite integral:

x(5x22)4dx

Let u=5x22, then derivative will be,

du=d(5x22)=10xdx

Rewrite the above integration as:

110(5x22)410xdx

Substitute du for 10xdx and u for 5x22 in provided integration.

110(5x22)410xdx=110u4du

Now apply, the power rule of integrals:

110

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