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Help with a trig integration

  1. May 19, 2010 #1
    1. The problem statement, all variables and given/known data
    integrate tan(x)sec^4(x) dx

    2. Relevant equations

    3. The attempt at a solution
    int tan(x)sec^4(x) dx
    = int tan(x)sec^2(x)sec^2(x) dx
    = int tan(x)sec^2(x) (tan^2(x)+1) dx

    let u = tanx ==> du = sec^2(x) dx

    = int usec^2(x) (u^2 + 1) /sec^2(x) du
    = int u(u^2+1) du
    = u^4/4 + u^2/2 + C
    and then replace the u with tanx

    am i doing this correct?
  2. jcsd
  3. May 19, 2010 #2

    Char. Limit

    User Avatar
    Gold Member

    Absolutely. If you want, you can unfactor the answer, but it isn't necessary.
  4. May 19, 2010 #3
    ttthank you!
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