# Integral of a function of trigonometric functions

I've been trying to solve the integral of the following function of cosines with Weierstrass substitution $$\int_{0}^{2\pi}\frac{\sqrt{\pi}S}{-S_2}\exp(S^2)(1+\text{erf}(S))\text{d}x$$ $$S=\frac{S_{1}}{2\sqrt{-S_{2}}}$$ $$S_{1}=A_{1}\cos(x+\delta_{1})$$ $$S_{2}=A_{2}\cos(2x+\delta_{2})+B_2\quad\quad (S_2<0)$$ As this is not a rational function of trigonometric functions, I failed. Which other techniques can I try to solve this? This integral is related to a previous attempt to integrate a 3D Gaussian.

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What makes you think, that this can be solved (whatever that means)? I mean, another way than numerically... –  draks ... Sep 27 '12 at 10:33
(whatever that means): solve this definite integral... As for this integral having an analytical solution: I'm not sure, I just wanted to ask whether anyone had an idea on how to approach this. –  Wox Sep 27 '12 at 11:07