efficient algorithm for numerical quadrature

[secondrate]

I have this function: (K_{i\mu} (z) = \frac{1}{\sinh{({\pi \mu}/2})} \int^\infty_0 \sin{(z \sinh{t})} \sin{(\mu t)} \,dt) which appears in a bond pricing formula I'm trying to implement in C++. The function inside the integral seems sinusoidal as it is a product of two sinusoidal functions (ie the function inside the integral is oscillating). Is there an efficient C++ code to best approximate this, taking into consideration that the upper limit is also infinity?

Thanks!

 

[koupparis]

Doesn't sinh blow up at infinity? In which case neither of the sin functions tend to zero, hence the integral can't converge.