# Integral of sec x

by Hyperreality
Tags: integral
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 P: 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.
 Sci Advisor HW Helper P: 1,995 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.
 P: 321 Yup. shmoe's method is the easiest one to remember.

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