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Thread: a problem about integral

  1. #1
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    a problem about integral

    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.
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  2. #2
    Super Member ILikeSerena's Avatar
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    Re: a problem about integral

    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
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  3. #3
    Senior Member vincisonfire's Avatar
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    Re: a problem about integral

    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?
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  4. #4
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    Re: a problem about integral

    No this is not taken from a book.
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