   Chapter 13.6, Problem 23E ### 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. ∫ e 2 x e x + 1 d x

To determine

To calculate: The value of the integral e2xex+1dx using integration by part.

Explanation

Given Information:

The provided integral is e2xex+1dx.

Formula used:

The formula for integration by parts is given by:

udv=uvvdu

Calculation:

Consider the provided integral:

e2xex+1dx

Rewrite the integral as,

exexex+1dx

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=ex

And,

dv=(ex+1)1/2exdx

Then,

du=exdx

And,

v=(ex+1)1/2exdx=23(ex+1)3/2

Then, use the formula for integration by parts:

udv=uvvdu

To obtain,

e2xex+1dx=23ex(ex+1)

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