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Integral of 1/sin^4x

  • #1

Homework Statement



integral of 1/(sinx)^4

Homework Equations



i dunno

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?
 

Answers and Replies

  • #2
ranger
Gold Member
1,676
1
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:
  • #3
682
1
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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