I am wondering whether the following integral
$$ Y = \int_{x_0}^{x_1} \exp{\left(a\cos x+b\sin x\right)}\,dx,$$
has a known closed form for given $a,b,x_0$ and $x_1$.
Since the exponential of the periodic function $a\cos x+b\sin x$ is also periodic, I know that this integral can be computed under a period, and the solution in terms of a modified Bessel function can be found here.
But, what about for general integral limits?
Thanks for any hint!