   Chapter 13.6, Problem 16E ### 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. ∫ x ln x   d x

To determine

To calculate: The value of the integral xlnxdx.

Explanation

Given Information:

The provided integral is xlnxdx.

Formula used:

The formula for integration by parts is given by:

udv=uvvdu

According to the power rule of integrals,

xndx=xn+1n+1+C

The differential formula,

d(lnx)dx=1x

Calculation:

Consider the provided integral:

xlnxdx

Now, split the integrand into two parts

Set one part equal to u and another part equal to dv.

So, the values will be,

u=lnx

And,

dv=xdx

Now use the differential formula d(lnx)dx=1x to differentiate u=lnx

du=1xdx

And integrate v by the use of power rule of integrals,

v=

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