Primitives

i just don't know how to primitivize very well

what should i do when i need to primitivize a fraction

could you please explain me clearly how this function was primitivized?
http://img369.imageshack.us/img369/1093/zzzls4.jpg

let t = tan(x), dt = sec^2(x)dx, 1+t^2 = sec^2(x)

the integral becomes: I[sin(x)dx/cos^2(x)]

let u = cos(x)... etc

the integral then becomes u^-1 => I = sec(x)

from above you have

t = tan(x)
=> cos(x) = (1+t^2)^-(1/2)
=> sec(x) = (1+t^2)^(1/2), as required