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A fairly easy integral

  1. Jan 27, 2012 #1
    1. The Problem comes down to what I think is a fairly simple integral, I just can't figure it out.

    int(x^2/(1+x^2)

    I know this is x-arctan(x)+c, but cannot figure out how.

    I tried subbing in u for x^2, this didn't really help me with a direction to take though.
     
  2. jcsd
  3. Jan 27, 2012 #2
    if you ever see a [itex]1+x^2[/itex] you should imediately think to yourself TRIG SUBSTITUTION!

    What relation do you know between [itex]sin^2[/itex] and [itex]cos^2[/itex]?

    I'd start there
     
  4. Jan 27, 2012 #3

    Ray Vickson

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    First, write f(x) = x^2/(1+x^2) as f(x) = (x^2 + 1 - 1)/(1+x^2) = 1 - 1/(1+x^2), so
    int(f(x)) = x - int(1/(1 + x^2)) The expression 1 + x^2 cries out for the substitution x = tan(t).

    RGV
     
  5. Jan 27, 2012 #4
    ANGER!!! I knew I was forgetting something really easy, like adding and subtracting one. Thanks for the help
     
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