Mathematics: Integrate : [1/{cos^2x(1-tanx)}^2]dx

Let,

I=∫[1/{cos^2x(1-tanx)}^2]dx

=∫[sec^2(x)/(1-tan(x))^2]dx

Put, 1-tan(x)=t

so, -sec^2(x)dx=dt



∴ I=-∫dt/t^2

=-[t^(-2+1)/(-2+1)]+C

=1/t+C

= 1/(1-tan(x))+C