I know the integral of sec x is ln|tan(x)+sec(x)|+C, but how would you do it? I tried all the techniques and tricks I've learnt and nothing came up.
Did you try multiplying by 1? [tex]sec(x)=\displaystyle sec(x)\frac{sec(x)+tan(x)}{tan(x)+sec(x)}=\displaystyle\frac{sec^{2}(x)+sec(x)tan(x)}{tan(x)+sec(x)}[/tex]. Your integral is now of the form [tex]\displaystyle\frac{f'(x)}{f(x)}[/tex], easy to handle.