Question

integral of 1/(1-cosx)????

Answer 1

multiply top and botom by conjugate (1-cosx)
int(1-cosx)/sin^2xdx
=intcsc^2x-intcosx/sin^2xdx
for 2nd part
use sub
u=sinx
du=cosxdx
sub
intcosx/sin^2xdx=intdu/u^2
=-1/u
=-1/sinx=-cscx
the answer is -cotx-cscx+c

Answer 2

Alternatively, you can use the half-angle substitution \(t=\tan\dfrac{x}{2}\) to determine an expression for \(\cos x\) in terms of \(t\) and end up with a rational function of \(t\).

Answer 3

@Lilium I believe you meant \(1+\cos x\) as the conjugate.