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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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Applying the General Power Rule In Exercises 21–32, find the indefinite integral. Check your result by differentiating.

x 2 ( x 3 4 ) 2 d x

To determine

To calculate: The indefinite integral x2(x34)2dx.

Explanation

Given Information:

The provided indefinite integral is x2(x34)2dx.

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(x34)2dx

Let u=x34, then derivative will be,

du=d(x34)=3x2dx

Rewrite integration as,

x2(x34)2dx=13(x34)23x2dx

Substitute du for 3x2dx and u for x34 in provided integration

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