I was wondering if someone could help me with the evaluation of an integral:
\begin{equation} \int_{x_1}^{x_2} \frac{e^{ax}}{\sqrt{1-b\cos(x)}}dx \end{equation}
I'm familiar with elliptic integrals of the first and second kinds, and I can obtain solutions for
\begin{equation} \int_{x_1}^{x_2} \frac{1}{\sqrt{1-b\cos(x)}}dx \end{equation}
or
\begin{equation} \int_{x_1}^{x_2} \sqrt{1-b\cos(x)} dx \end{equation}
but I am not sure how to deal with the exponential in the numerator. Any help will be much appreciated.