0
$\begingroup$

Possible Duplicates:
Evaluating $\\int P(\\sin x, \\cos x) \\text{d}x$
Ways to evaluate $\int \sec \theta \, \mathrm d \theta$

Using Mathematica to get the antiderivative for sec(x), I get $$-\log(\cos\frac{x}{2}-\sin\frac{x}{2})+\log(\cos\frac{x}{2}+\sin\frac{x}{2}).$$

This doesn't look familiar, so, I'm thinking there's probably some identity or other way to transform this...

Any insight would be appreciated.

  • 2
    This falls under http://math.stackexchange.com/questions/29980/evaluating-int-p-sin-x-cos-x-textdx2011-03-31
  • 0
    For $\sec(x)\tan(x)$, this is the derivative of $\sec(x)$. For $\sec(x)$ it's more complicated, but Weierstrass substitution works (in the worse case scenario).2011-03-31
  • 0
    @Arturo: I updated 29980 to include rational functions. I believe your current answer addresses that, but notifying you, just in case you think it might need editing.2011-03-31
  • 0
    @NateyG: No, there is no particularly simpler form, though some tables list it as $\log(\sec x + \tan x)+C$, $\log(\tan(\frac{x}{2}+\frac{\pi}{4})) + C$, or $\frac{1}{2}\ln|\sin x + 1| - \frac{1}{2}\ln|\sin x - 1| + C$.2011-03-31
  • 2
    The Antiderivative of $\sec(x)$ was already asked in this question http://math.stackexchange.com/questions/6695/ways-to-evaluate-int-sec-theta-d-theta/6717#6717 "ways to evaluate integral sec"2011-03-31
  • 0
    Ah thanks. I need to do a better job of searching next time. ><2011-03-31

2 Answers 2