Integral of sec x

  1. 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. jcsd
  3. shmoe

    shmoe 1,994
    Science Advisor
    Homework Helper

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