   Chapter 5, Problem 27RE ### 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
1 views

# Applying the General Power Rule In Exercises 21–32, find the indefinite integral. Check your result by differentiating. ∫ 4 x 2 ( 3 x 3 + 1 ) 2   d x

To determine

To calculate: The indefinite integral 4x2(3x3+1)2dx.

Explanation

Given Information:

The provided indefinite integral is 4x2(3x3+1)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:

4x2(3x3+1)2dx

Let u=3x3+1, then derivative will be,

du=d(3x3+1)=9x2dx

Rewrite integration as,

4x2(3x3+1)2dx=49(3x3+1)2(9x2dx)

Substitute du for 9x2dx and u for 3x3+1 in provided integration

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