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Indefinite integral and anti-derivative

  1. Jan 25, 2010 #1
    1. The problem statement, all variables and given/known data

    Find the indefinite integral of 16x^2+36+1/(16x^2+36) with respect to x

    2. Relevant equations

    Anything possible to take an anti-derivative

    3. The attempt at a solution

    I have absolutely no idea on how to deal with this problem. I can take an anti-derivative of the first 2 terms just fine but that fraction term just messes with me. I don't know how to take it on. It kind of looks like 1/(1+x^2) which would have an anti-derivative of arctan(x) but I really don't know how to handle this.

    Thanks for the help:smile:
  2. jcsd
  3. Jan 25, 2010 #2

    Char. Limit

    User Avatar
    Gold Member

    If it looks like 1/(1+x^2), then maybe you should make it look more like such by factoring things out, and do a trig substitution.

    Also, have you tried using partial fractions?
  4. Jan 25, 2010 #3
    I've tried a bunch of ways to try to solve this. Of my whole homework set, this is the only one I can't get. I just don't see how to break apart that fraction.
  5. Jan 25, 2010 #4


    Staff: Mentor

    You can't break apart that fraction. You need to make it look like 1/(a^2 + u^2), which has an antiderivative of arctan(u/a) + C.
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