Question

integrate sin^xcosec^x dx

Answer 1

Answer:

Can't see very clearly with the indices that you have written. I will assume the one close to sine is -2 and the one close to cosecant is 2:

$\int \:sin^{-2}x\cdot csc^2xdx=\int \:csc^4xdx=-\frac{1}{3}\left(csc^2x\cdot cotx\right)+\frac{2}{3}\int \:csc^2xdx=-\frac{1}{3}csc^2xcotx-\frac{2}{3}\left(1\right)\left(csc^0x\cdot cotx\right)+0\int csc^0xdx=-\frac{1}{3}csc^2xcotx-\frac{2}{3}cotx=\left(-\frac{1}{3}cotx\right)\left(csc^2+2\right)$

The technique here is to use reduction formula.

Hope it helps :)

Step-by-step explanation: