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Homework Help: Stuck on the integral: arctan (4t) dt

  1. Aug 29, 2012 #1
    1. The problem statement, all variables and given/known data

    The Integral is arctan (4t) dt

    2. Relevant equations

    I know how to do integration by parts, but I guess I have forgotten some of the integration rules.

    3. The attempt at a solution

    I set ∫arctan(4t)=u, and dt=dv

    I know that the derivative of arctan(x) is 1/(1+x^2), But when I differentiate arctan(4t), it comes out as 4t/(1+16t^2). Why is this? To me it seems like it should be 1/(1+4t^2). I know how to do the rest, I have the answer, I'm just not sure how they got there. Thanks for any help.
  2. jcsd
  3. Aug 29, 2012 #2


    User Avatar
    Homework Helper
    Gold Member

    Because you've calculated the derivative wrong. To tell you exactly where your error is, you'll need to post your steps.
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