Chapter 8.2, Problem 65E

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# Using Two Methods Together In Exercises 63-66, find the indefinite integral by using substitution followed by integration by parts. ∫ x 5 e x 2   d x

To determine

To calculate: The indefinite integaral x5ex2dx with the help of substituation followed by integration by part.

Explanation

Given:

The provided expression is âˆ«x5ex2dx.

Formula used:

Integration by part âˆ«udv=uvâˆ’âˆ«duâ‹…v.

Calculation:

The given integration is I=âˆ«x5ex2dx.

Substitute,

t=x5x=t15dx=15dt

From the integration,

I=15âˆ«t15et25dt â€¦â€¦ (1)

Again substitute,

p=t25t=p52dt=52dp

Therefore,

I=(12)(52)âˆ«epp2dp â€¦â€¦ (2)

Integrate on right hand side by using integration by parts.

Let,

u=p2du=2pdp

And

dv=epv=ep

Now, substitute these values in the formula for integration by parts

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