The following integral
$$\int\limits\_0^\infty \frac{\cos{\left(\frac{1}{2}\sqrt{3}s\right)}}{\sqrt{\cosh{s}-\cos{\theta}}}\,ds$$
can be found in the paper 



> 
> Tevian Dray and Gerard 't Hooft, *The gravitational shock wave of a massless particle*, Nuclear Physics B **253** (1985) 173--188, doi:[10.1016/0550-3213(85)90525-5](http://dx.doi.org/10.1016/0550-3213%2885%2990525-5). 
> 
> 
> 


They write that they "have not attempted to perform the integration explicitly". Was this integral ever calculated explicitly?



Calculation of the integral related to the gravitational shock wave
A closed form exists in Gradshteyn and Ryzhik, 8.842.1.



> 
> As a comment to this answer:
> 
> 
> Referring to the Gradshteyn and Ryzhik, the following result is given in <http://arxiv.org/abs/hep-th/9408169> (On Gravitational Shock Waves in Curved Spacetimes, by K. Sfetsos):
>  $$\int \limits\_0^\infty \frac{\cos{(\sqrt{c-1/4}\,s)}}{\sqrt{\cosh{s}-\cos{\theta}}}\,ds=\frac{\pi}{\sqrt{2}\cosh{(\sqrt{c-1/4}\,\pi)}}F\left(\frac{1}{2}-i\sqrt{c-1/4},\frac{1}{2}+i\sqrt{c-1/4},1,\cos^2{\frac{\theta}{2}}\right)=\frac{\pi}{\sqrt{2}\cosh{(\sqrt{c-1/4}\,\pi)}}P\_{-1/2+i\sqrt{c-1/4}}(-\cos{\theta}).
> $$
> 
> 
> 


