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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 9–34, find the indefinite integral. Check your result by differentiating. See Examples 1, 2, 3, and 5.

( 4 x 3 + 8 x ) 3 ( 3 x 2 + 2 ) d x

To determine

To calculate: The indefinite integral of (4x3+8x)3(3x2+2)dx and check the result by differentiating.

Explanation

Given Information:

The indefinite integral is (4x3+8x)3(3x2+2)dx.

Formula used:

General Power Rule:

If u is a differentiable function of x, then

undudxdx=undu=un+1n+1+c,n1

The Power Rule:

ddxxn=nxn1

Where n is a real number.

Calculation:

Consider indefinite integral,

(4x3+8x)3(3x2+2)dx

Let u=4x3+8x,

So,

du=(12x2+8)dx=4(3x2+2) dx

Now use the general power rule to get,

(4x3+8x)3(3x2+2)dx=14u3du

Now the integral will be:

14u3du=14u3+13+1+C=14u44+C=u416+C

Substitute back the value of u to get,

(4x3+8x)

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