Integral Equation: Solve & Find Laplace Transform

[ber70]

$$\frac{1}{\pi}\int^{\pi}_{0}cos(n\theta - xsin\theta)d\theta$$
How can I solve this equation and find Laplace transform?

 

[fzero]

Use the trig identity for sums of angles. The resulting integrals can probably be related to Bessel functions.