   Chapter 13.6, Problem 9E ### 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 1-16, use integration by parts to evaluate the integral. ∫ 1 e In  x   d x

To determine

To calculate: The value of the integral 1elnxdx with the help of integral by parts.

Explanation

Given Information:

The provided integral is 1elnxdx.

Formula used:

The formula for integration by parts is given by:

udv=uvvdu

For any variable u, the integral formula is,

undu=un+1n+1+C

Calculation:

Consider the provided integral:

1elnxdx

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=lnx

And,

dv=dx

Then, differentiate u=lnx on both sides with respect to u,

du=1xdx

Also, integrate the equation dv=dx by the use of formula undu=un+1n+1+C

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