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Integral of sec x

by Hyperreality
Tags: integral
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Hyperreality
#1
Aug8-04, 11:49 PM
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.
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shmoe
#2
Aug9-04, 12:22 AM
Sci Advisor
HW Helper
P: 1,994
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
#3
Aug9-04, 01:10 AM
P: 321
Yup. shmoe's method is the easiest one to remember.


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