What is the easiest way to solve this integral with u-subsitition or what are other methods should be used? How would you calculate this integral?


Gigantic hint: $$\int_{0}^{\pi/2}\frac{\sin^{45}(x)}{\sin^{45}(x)+\cos^{45}(x)}+\int_{0}^{\pi/2}\frac{\cos^{45}(x)}{\sin^{45}(x)+\cos^{45}(x)}=\frac{\pi}{2}$$ How are those two integrals related? (think u-substitution)
