Question

Integrate csc^4x/cot^2x

Answer 1

Hello,


`1) \int\limits (1)/(sin^2(x)) \, dx =-\ cotg x\\\\ 2)cosec^4(x)/cotg^2(x)= (1)/(sin^4(x)) * (sin^2(x))/(cos^2(x))= (4)/(sin^2(2x)) \\\\\\ \int\limits{cosec^4(x)/cotg^2(x)} \, dx \\\\ = \int\limits{ (4)/(sin^2(2x))} \.dx\\\\ =-\ 2\ cotg(2x) + C`