# Integral of sec x

1. ### Hyperreality

203
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.

2. ### shmoe

1,994
Did you try multiplying by 1?

$$sec(x)=\displaystyle sec(x)\frac{sec(x)+tan(x)}{tan(x)+sec(x)}=\displaystyle\frac{sec^{2}(x)+sec(x)tan(x)}{tan(x)+sec(x)}$$. Your integral is now of the form $$\displaystyle\frac{f'(x)}{f(x)}$$, easy to handle.

3. ### Corneo

321
Yup. shmoe's method is the easiest one to remember.