$$\displaystyle\int{ \frac{ 1 }{ 12 \cos x-5 \sin x } }d x$$
$\frac{\ln(|2\tan(\frac{x}{2})+3|)}{13}-\frac{\ln(|-3\tan(\frac{x}{2})+2|)}{13}+С$
$\frac{\frac{\mathrm{d}}{\mathrm{d}x}(\tan(\frac{x}{2}))}{\left(-3\tan(\frac{x}{2})+2\right)\left(2\tan(\frac{x}{2})+3\right)}$
