Integral of sec x

Hyperreality

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.

shmoe

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.

Corneo

Yup. shmoe's method is the easiest one to remember.