I struggle to solve the following definite integral: \begin{equation} \int_{-a}^{a} e^{\frac{1}{c_0+c_1\cdot cos(x)}} \mathrm{d}x \end{equation}
where $c_0\neq 0$, $c_1\neq 0$ and $a > 0$
The substitution approach to a linear expression in the exponential doesn't seem to lead anywhere. Numerical integration is not an option, as the result needs to be calculated dynamically on low power hardware.
Is there a closed form solution to this problem? If not, what would be your suggestion for an approximation?
Thanks for any comments,
Peter
