Integral of a squared sum of sin + exponential

42 Views Asked by At

What is the best way to solve this integral?

$$\int_{0}^{\pi/2}\bigg(\frac{\sin^{2}\left(x\right)}{\sin^{2}\left(x\right)+c_{1}}e^{m\frac{\sin^{2}\left(x\right)}{\sin^{2}\left(x\right)+c_{1}}} + \frac{\sin^{2}\left(x\right)}{\sin^{2}\left(x\right)+c_{2}}e^{m\frac{\sin^{2}\left(x\right)}{\sin^{2}\left(x\right)+c_{2}}} \bigg)^2dx$$

Tips or suggestion are appreciated.

I am able to find the integral of each component separately but not the square of their sum.