Please help me with the following integral please simplify it and then solve

Integral of (sec x)/(sec x+tan x)^2 dx.....(1)take sec x+tanx=t(sec x tan x+sec^2x)dx=dtsec x (sec x+tan x)dx=dtdx=dt/(sec x (sec x+tanx)putting value of dx in (1) we getintegral of dt/t^3 =(-1/2)(sec x+tanx)^2