   Chapter 13.6, Problem 21E ### 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  ln  x  d x

To determine

To calculate: The value of the integral x3ln2xdx using integration by part.

Explanation

Given Information:

The provided integral is x3ln2xdx.

Formula used:

The formula for integration by parts is given by:

udv=uvvdu

Calculation:

Consider the provided integral:

x3ln2xdx

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)2

And,

dv=x3dx

Then,

du=2lnxxdx

And,

v=x3dx=x44

Then, use the formula for integration by parts:

udv=uvvdu

To obtain,

x3ln2xdx=14x4(lnx)212x3lnxdx

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

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