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-   -   Indefinate integral for trig function (https://www.askmehelpdesk.com/showthread.php?t=186773)

  • Feb 21, 2008, 06:50 PM
    interinfinity
    indefinate integral for trig function
    I would like to know how to set up this specific integral...
    I don't know how to do an integral symbol on here...

    I need the integral of : cos^2(x)tan^5(x)
    that's... cosine squared x times tangent fifth x

    I have tried doing it by integration by parts, but that won't work because the integral of either part is tricky to get without a graphing calculator.

    I'm trying to use trig identities, the only thing I can come up with is breaking tan^5(x) up into secent... OK I admit it I don't have a clue what I'm talking about. I hate trig. If no one responds to this post I won't shed a tear, I hate trig.
  • Feb 22, 2008, 04:53 AM
    galactus
    Wow, finally a problem with a little meat to it. Something besides the usual "Help me solve x=4 for x".

    A lot of times these things take some insight to see the substitution. Besides, trig is cool.

    I was a surveyor for years and used it everyday. I didn't have to integrate trig functions, but I used it.



    Make the sub

    Then you get



    Now, if you let

    Note that

    It whittles down to something fairly easy to integrate.


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