integrating exponential with power of trigonometric functions

43 Views Asked by At

I'm stuck with the bellow integral and couldn't find any solution, If anyone has an idea how to continue I'll be very grateful.

(1)\begin{equation} \int_{0}^{2\pi} e^{a\cdot\sin2\theta+b\cdot\cos(\theta-\mu)}d\theta \end{equation}

I know that

(2) $$\int_{0}^{2\pi} e^{a\cdot\sin\theta+b\cdot\cos\theta}d\theta={2\pi I_0(\sqrt{a^2+b^2})}$$

but couldn't find any way to get from (1) to (2)

Thank you very much!