Solving Integral of 1/(sinx)^4

[fizzzzzzzzzzzy]

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?

 

[ranger]

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

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).

 

[tim_lou]

hints:
1. think about csc(x)

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

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