   Chapter 5.2, Problem 18E ### 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. ∫ − 12 x 2 ( 1   -   4 x 3 ) 2   d x

To determine

To calculate: The value of the provided indefinite integral 12x2(14x3)2dx.

Explanation

Given Information:

The provided indefinite integral is 12x2(14x3)2dx.

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

and

am=1am

Calculation:

Consider the indefinite integral say I,

I=12x2(14x3)2dx

Let

14x3=u … (1)

Differentiate the above equation with respect to x;

ddx(14x3)=dudxddx(1)ddx(4x3)=dudx(12x2)=dudx

Or

(12x2)dx=du … (2)

Substitute the values of 14x3 and (12x2)dx from equations (1) and (2) respectively in the provided integral;

I=

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