What is the best way to solve this integral?
$$\int_{0}^{\pi/2}\prod_{i=1}^{N=2}\frac{\sin^{2}\left(x\right)}{\sin^{2}\left(x\right)+c_{i}}e^{m\frac{\sin^{2}\left(x\right)}{\sin^{2}\left(x\right)+c_{i}}}dx$$
or
$$\int_{0}^{\pi/2}\frac{\sin^{4}\left(x\right)}{\left(\sin^{2}\left(x\right)+c_{1}\right)\left(\sin^{2}\left(x\right)+c_{2}\right)}e^{m\frac{\sin^{2}\left(x\right)}{\sin^{2}\left(x\right)+c_{1}}}e^{m\frac{\sin^{2}\left(x\right)}{\sin^{2}\left(x\right)+c_{2}}}dx$$
Tips or suggestion are appreciated.