Compute
$\displaystyle \int_0^{\pi/2}\frac{\sin x}{9+16\sin(2x)}\,dx$
Use the substitutions...
$\displaystyle t= \tan \frac{x}{2}$
$\displaystyle dx = 2\ \frac{dt}{1+t^{2}}$
$\displaystyle \sin x = \frac{2 t}{1+t^{2}}$
$\displaystyle \cos x = \frac{1-t^{2}}{1+t^{2}}$
... and take into account the identity...
$\displaystyle \sin 2x = 2\ \sin x\ \cos x$
Kind regards
$\displaystyle \chi$ $\displaystyle \sigma$