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Math Help - Integral question relating to arctan...

  1. #1
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    Integral question relating to arctan...

    How do you do this integral?

    \int \frac {x^2}{1+x^2} dx

    The original problem was \int x tan^{-1}x.

    By doing integration by parts, I got \int \frac {x^2}{1+x^2} dx as an integral later on.

    But when I try integration by parts on this second integral, I end up having to evaluate \int x tan^{-1}x again, and getting into a never-ending cycle is never a good idea.

    Any ideas?
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  2. #2
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    \frac{x^2}{x^2+1} = \frac{x^2+1-1}{x^2+1} = \frac{x^2+1}{x^2+1} - \frac{1}{x^2+1} = 1 - \frac{1}{x^2+1}

    now integrate
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  3. #3
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    That's a really neat solution. Thanks!
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