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Math Help - Antiderivative

  1. #1
    Junior Member
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    Antiderivative

    How do you find this antiderivative?

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

    I see that the x^2 +1 looks like the derivative of tan^{-1}(x), but I don't know how to antidifferentiate that equation. :/
    Last edited by Jhevon; January 29th 2009 at 09:04 PM. Reason: Please do not delete your question after it has been answered
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  2. #2
    Super Member
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    Quote Originally Posted by Cursed View Post
    How do you find this antiderivative?

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

    I see that the x^2 +1 looks like the derivative of tan^{-1}(x), but I don't know how to antidifferentiate that equation. :/
    Add 1 and subtract 1 to get:

    \int \frac{x^2+1-1}{x^2+1}~dx = \int \frac{x^2+1}{x^2+1}~dx - \int \frac{1}{x^2+1}~dx

    \ldots
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