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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.

x 2 ( 3 x 3  +  8 ) 2   d x

To determine

To calculate: The value of the provided indefinite integral x2(3x3+8)2dx.

Explanation

Given Information:

The provided indefinite integral is x2(3x3+8)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=x2(3x3+8)2dx

Multiply and divide by 9 in the right-hand side of above integral

I=199x2(3x3+8)2dx

Take the factor 19 out of the integrand

I=199x2(3x3+8)2dx

Let

3x3+8=u … (1)

Differentiate the above equation with respect to x

ddx(3x3+8)=dudxddx(3x3)+ddx(8)=dudx(9x2)=dudx

Or

(9x2)dx=du … (2)

Substitute the values of 3x3+8 and

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