   Chapter 5.2, Problem 14E ### 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. ∫ ( x 4  +  3 x 2 ) ( 4 x 3   +   6 x )   d x

To determine

To calculate: The value of the provided indefinite integral (x4+3x2)(4x3+6x)dx.

Explanation

Given Information:

The provided indefinite integral is (x4+3x2)(4x3+6x)dx.

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

Calculation:

Consider the indefinite integral say I,

I=(x4+3x2)(4x3+6x)dx

Let

x4+3x2=u … (1)

Differentiate the above equation with respect to x;

ddx(x4+3x2)=dudxddx(x4)+ddx(3x2)=dudx4x3+6x=dudx

Or

(4x3+6x)dx=du … (2)

Substitute the values of x4+3x2 and (4x3+6x)dx from equations (1) and (2) respectively in the provided integral;

I=

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