3. Calculate

$$
\int \frac{3 \sin x + 2 \cos x}{3 \cos x + 2 \sin x} d x, \quad x \in \left(0, \frac{\pi}{2}\right)
$$
Solution. Find $a, b$ such that

$$
3 \sin x+2 \cos x=a(3 \cos x+2 \sin x)+b(3 \cos x+2 \sin x)^{\prime}
$$

## We obtain

$$
\int \frac{3 \sin x+2 \cos x}{3 \cos x+2 \sin x} d x=\frac{1}{13}(12 x-\ln (2 \sin x+3 \cos x))+\mathcal{C}
$$