Question: $$\int\_0^\frac{\pi}{2}(\sin^3x +\cos^3x) \, \mathrm{d}x$$

How do I compute this? I tried to do the trigonometric manupulation but I can't get the answer.

Answer: 
Applying **[this](https://en.wikipedia.org/wiki/Integration_by_reduction_formulae)** should give you your answer in no time!
**Hint:** Use partial integration a couple of times.