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Homework Help: Integral of 1/sin^4x

  1. Mar 1, 2007 #1
    1. The problem statement, all variables and given/known data

    integral of 1/(sinx)^4

    2. Relevant equations

    i dunno

    3. The attempt at a solution

    ive tried substitution but that just results in a more complicated integral, integration by parts does the same thing without actually reducing the integral. I though i could use integration by parts to recreate the original integral but, i can't get that to work either. any help?
     
  2. jcsd
  3. Mar 1, 2007 #2

    ranger

    User Avatar
    Gold Member

    This looks like something where you would do Wierstrass substitution.
    http://math.berkeley.edu/~reshetik/LN/1B-lec6.pdf [Broken]

    t=tan(x/2); sin(x) = 2t/(1+t2); then figure out what dx so you can replace it with dt. After you've integrated, remember that t=tan(x/2).
     
    Last edited by a moderator: May 2, 2017
  4. Mar 1, 2007 #3
    hints:
    1. think about csc(x)

    not enough?
    2. think about 1+csc^2(x)

    still not enouh?
    3. think about d(cot(x))
     
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