Question

What is `int sin x/ ( 1-cos^2x)dx`?

Answer 1

`ln|cosecx-cotx|+C`

Explanation:

From trig identities, `sin^2x+cos^2x=1`

Hence the integral may be written and solved as follows :

`intsinx/(1-cos^2x)dx=intsinx/sin^2xdx=int1/sinxdx=intcosecxdx`

`=ln|cosecx-cotx|+C`