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Powers or Trig Functions Question - Integral

  1. Jun 18, 2008 #1
    1. The problem statement, all variables and given/known data
    Integral of : (sec x)^5 (tan x)^3 dx


    2. Relevant equations
    I am having trouble substituting correctly for this equation and i cant get it to work. I believe it has to do with trig powers ?

    If anyone could help be step by step. or even just a hint on how to solve it that would be great.

    Thanks in advance !
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jun 18, 2008 #2

    Gib Z

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    Homework Helper

    Welcome to PF!

    My Hint would be to rewrite the tan cubed term in terms of a square and a linear, then change the square term with a Pythagorean identity, expand and see where that takes you.
     
    Last edited: Jun 18, 2008
  4. Jun 18, 2008 #3
    You should probably memorize this rule for integrating trigonometric integrals

    For any [tex]\int{tan^{m}xsec^{n}xdx}[/tex]

    If n is even, substitute u = tan(x)
    If m is odd, substitute u = sec(x)
    If m is even, n is odd, reduce to powers* of sec(x)
    Also, using the identity [tex]1+tan^{2}x=sec^{2}x[/tex] is helpful in all three cases
     
    Last edited: Jun 18, 2008
  5. Jun 18, 2008 #4
    Thank you very much for all your help. I just finished solving the problem.

    Its alot easier using the hints you provided! Thanks!:smile:
     
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