# Integral of sec x

1. Aug 8, 2004

### 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.

2. Aug 9, 2004

### shmoe

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. Aug 9, 2004

### Corneo

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