text: integrate sin(x)/(1+cos^2(x))?   you have to use substitution.  let u = cos(x) du = -sin(x) dx, so -du = sin(x)dx  therefore, your new integral becomes:  -1 / (1 + u^2)  and integrating that, you get  - tan(inverse) (u)  resubstituting u=cos(x), you get  -tan(inverse) (cos(x))