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Trig Integral

  1. Feb 5, 2009 #1
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
    1. The problem statement, all variables and given/known data

    2. Relevant equations
    u = 1+tant
    du = sec^2(t) dt
    dt = du / sec^2(t)

    3. The attempt at a solution

    It seems like I should be using substitution in the equation, however the exponent is messing things up for me. I recall from derivatives how they interact with the chain rule, but am not sure how this would work backwards in integration. Something like,

    I(u^3)(sec^2(t)) = (u^4/4)((sec^2(t)) (tan(t))

    Except I haven't gotten rid of the t variable and now have t and u. Any points are welcome.
  2. jcsd
  3. Feb 5, 2009 #2
    Why don't you just substitute u for (1 + tan t) and du for sec^2(t) dt (and take care of the limits of integration, of course)?
  4. Feb 5, 2009 #3
    Ah I see how when I change the limits of integration it removes the nasty sec^2(t) so all i'm left with is the integral of u^3 with u going from 1 to 2. Thanks.
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