   Chapter 13.6, Problem 24E ### 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. ∫ 1 2 ( ln  x ) 2 d x

To determine

To calculate: The value of the integral 12(lnx)2dx using integration by part.

Explanation

Given Information:

The provided integral is 12(lnx)2dx.

Formula used:

The formula for integration by parts is given by:

udv=uvvdu

Calculation:

Consider the provided integral:

12(lnx)2dx

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=dx

Then,

du=2lnxxdx

And,

v=dx=x

Then, use the formula for integration by parts:

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