integrate dx/tanxcos^2x

sinx=u and du=cosxdx and dxcosx/sinxcos^2x then du/u(1-u)^2

1/u+1/1-u+1/1+u

a/u + b/1-u + c/1+u

I found c=-1/2, a=1 and b=1/2

ln|u|+1/2ln|1-u|-1/2ln|1+u|

ln|sinx|+1/2ln|1-sinx|-1/2ln|1+sinx|

ln|sinx|+ln|1-sinx|/1/2ln|1+sinx|

and I got stuck here.How can I solve that?