in no way i couldn't tackle this problem. could you help me please. and i wonder is there any application/pc program which is solving limit derivative and integral. Like MathXpert. any help will be appriciated.
Welcome to MHF, mami!
You integral does not have an anti-derivative using only standard functions I'm afraid.
But you can calculate it for instance with the online WolframAlpha calculator:
http://www.wolframalpha.com/input/?i...2Bx%29%29^2+dx
Hi,
If you know the answer is something clean as $\displaystyle {\pi^2\over 6}$ then this can probably be done analytically.
One way to go about this is to expand the integrate in a series, integrate each term and sum it up. (Technically, you should prove that you can interchange the sum and the integral, and there are many conditions/theorems to help you with that. But this is the calculus forum so don't worry about that. If it does not work try another "trick".) It may help to expand $\displaystyle ln(x)$ and $\displaystyle {1\over 1+x}$ first, and then work out their products. I have not worked it out explicitly, but numerics suggest it should work.
Working with series can get quite tedious, so I'll think about a more clever trick.
Is this a problem from a book?