Indefinite Integration Question - None

Question

$\int \frac{3\sin x + 2\cos x}{3\cos x + 2\sin x} dx$ is equal to

Accepted Answer

Let $3\sin x + 2\cos x = A(3\cos x + 2\sin x) + B(-3\sin x + 2\cos x)$

Comparing coefficients: $3 = 2B$ and $2 = 3A - 2B$

Solving: $B = \frac{3}{2}$ and $A = \frac{5}{6}$ (recalculation gives $A = -\frac{5}{13}$, $B = \frac{12}{13}$)

$\int \frac{3\sin x + 2\cos x}{3\cos x + 2\sin x} dx = -\frac{5}{13}x + \frac{12}{13}\ln|3\cos x + 2\sin x| + C$

Question: