Ta có:
$\int\limits_{\frac{-\pi}{2}}^{\frac{\pi}{2}}\sin2x\sin3xdx$
$=\int\limits_{\frac{-\pi}{2}}^{\frac{\pi}{2}}\dfrac{\cos x-\cos 5x}{2}dx$
$=\left(\dfrac{\sin x}{2}-\dfrac{\sin5x}{10}\right)\left|\begin{array}{l}\dfrac{\pi}{2}\\\dfrac{-\pi}{2}\end{array}\right.=\dfrac{4}{5}$