definite integral of ln^2(x) dx from 1 to e

[mathe25]

i have to calcute integral ln^2(x) dx= ?
lower limit is 1
upper limit is e

 

[srmichael]

i have to calcute integral ln^2(x) dx= ?
lower limit is 1
upper limit is e

Have you learned integration by parts? That's the ticket to this one. Um, and you'll have to use integration by parts twice on this one.

 

[mathe25]

no i have not

 

[srmichael]

Hmmm, not the answer I expected. So was this assigned by your teacher? Not sure how he would expect you to do this one if you have not learned Integration by Parts.

What's the title of the section of the textbook that this problem is in?

 

[DrPhil]

no i have not

Let's be sure we have the problem transcribed correctly:

\(\displaystyle \displaystyle \int_1^{\mathrm e} \ln^2(x)\ \mathrm d x \)

Is that right? The natural log is squared? If so, I don't see any way around the use of "integration by parts."