How to calculate $\int_0^\frac{\pi}{2}(\sin^3x +\cos^3x) \, \mathrm{d}x$? $$\int_0^\frac{\pi}{2}(\sin^3x +\cos^3x) \, \mathrm{d}x$$
How do I compute this? I tried to do the trigonometric manupulation but I can't get the answer.

$\int\sin^3xdx=\int\sin^2x\sin(x)dx=-\int(1-\cos^2x)d\cos x$
