   Chapter 13.6, Problem 20E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# In Problems 17-24, use integration by parts to evaluate the integral. Note that evaluation may require integration by parts more than once. ∫ x 3 e x d x

To determine

To calculate: The value of the integral x3exdx using integration by part.

Explanation

Given Information:

The provided integral is x3exdx.

Formula used:

The formula for integration by parts is given by:

udv=uvvdu

Calculation:

Consider the provided integral:

x3exdx

Now, split the integrand into two parts setting one part equal to u and another part equal to dv.

So, the values will be:

u=x3

And,

dv=exdx

Then,

du=3x2dx

And,

v=exdx=ex

Then, use the formula for integration by parts:

udv=uvvdu

To obtain,

x3exdx=x3ex3x2exdx …… (1)

Now, again split the second integrand into two parts setting one part equal to u and another part equal to dv.

So, the values will be:

u=x2

And,

dv=exdx

Then,

du=2xdx

And,

v=exdx=ex

Then, use the formula for integration by parts:

udv=uvvdu

To obtain,

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