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Thread: show the way

  1. #1
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    show the way

    How does one carry out

    \int\frac{1}{(x^2+1)^2}dx
    Last edited by CaptainBlack; Oct 14th 2009 at 05:08 AM. Reason: Added [tex][/tex] tags and corrected LaTeX
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  2. #2
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    - Wolfram|Alpha

    Click on 'show steps'

    Edit:

    Just in case a picture helps...



    ... where



    ... is the chain rule. Straight continuous lines differentiate downwards (integrate up) with respect to x, and the straight dashed line similarly but with respect to the dashed balloon expression (the inner function of the composite which subject to the chain rule).

    Carry on the anti-clockwise journey (to I) by finding G(theta) and mapping back from tan(theta) to x.


    __________________________________________

    Don't integrate - balloontegrate!

    http://www.ballooncalculus.org/examples/gallery.html

    http://www.ballooncalculus.org/asy/doc.html
    Last edited by tom@ballooncalculus; Oct 14th 2009 at 05:33 AM.
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  3. #3
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    Quote Originally Posted by nthethem View Post
    How does one carry out

    \int\frac{1}{(x^2+1)^2}dx
    What Tom@ballooncalculus is saying, in his own unique way, is that, since tan^2(u)+ 1= set^2(u), use the substitution tan(u)= x.
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