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Math Help - Last Integration Problem...I Swear!

  1. #1
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    Red face Last Integration Problem...I Swear!

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

    I know that the bottom is going to end up being
    \arctan{2x}

    but how do I get rid of the x^2
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  2. #2
    MHF Contributor matheagle's Avatar
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    I would rewrite this and then do some algebra

    Quote Originally Posted by summermagic View Post
    \int\frac{x^2}{1+4x^2} dx

    I know that the bottom is going to end up being
    \arctan{2x}

    but how do I get rid of the x^2
    Then  \int\frac{x^2}{1+4x^2} dx= (1/4)\int\frac{4x^2}{1+4x^2} dx= (1/4)\int\frac{(4x^2+1)-1}{1+4x^2} dx

    Then divide and integrate...

    (1/4)\int\ \biggl(1-{1\over 1+4x^2}\biggr) dx
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