Calculus problem?

Question

What's the integrals of "cosec^3 (x) dx". I can't solve this.But i know the answer that is:"-1/2cosec x cot x+1/2ln(tanx/2)+C"from a book..But I don't understand how can solve this problem and how my answer will be right?

Answer 1

cosec^3 (x) = 1/(sin^3(x))

so re-write it in terms of sin and cosine and solve. You've got an odd power of sin, so use the sin^2(x) + cos^2(x) = 1 identitiy, save a sin factor, substitute in, and go from there. Now do u-subs where u = cos (x)....etc.