Integral of sec x: Solving Techniques and Tricks

[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 learned and nothing came up.

 

[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.

 

[Corneo]

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