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Integral trig function

  1. Jun 17, 2012 #1

    shn

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    i have try to intergral cos^2( x)/sinx. When i used sinx=t i got {[(1-t^2)^n-(1/2)]\t}. When i use intergral by parts i got {cos^2n-1(x)[1-cos^2(x)]} to intergral. If you could give me a tip to intergral this i would bn thankful to you!
     
    Last edited by a moderator: Jun 17, 2012
  2. jcsd
  3. Jun 17, 2012 #2
    Where did the n come from? There is no n in the initial question.

    If I were you I would start by writing this as:

    [tex] \int cot(x)cos(x)dx [/tex]

    What identities do you know for cot(x) that might make this easier?

    edit - Your post changed during the time I was writing this. Yes, the way it is now written is actually easier to see the next step.
     
  4. Jun 17, 2012 #3

    shn

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    thankz man!i did'nt read it correctly!:'(
     
  5. Jun 17, 2012 #4

    Mark44

    Staff: Mentor

    First off, there is no such word in English as "intergral."

    And you don't "integral" something - you integrate it.

    Regarding your answers, n should not appear in them, so you are not using integration tables correctly, assuming that's what you're doing.

    The simplest way to approach this problem is to replace cos2(x) by 1 - sin2(x), which changes the integral you started with to
    $$ \int \frac{1 - sin^2(x)}{sin(x)}~dx$$

    Split this into two integrals and the rest is pretty straightforward.
     
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