Question

Evaluate $\int \frac{2\cos x-3\sin x}{6\cos x+4\sin x}dx$

Answer 1

Given integral is written as $\frac{1}{2}\int \frac{2cosx-3sinx}{3cosx+2sinx}$. The integral is of the form $\int \frac{f^{\prime }\left(x\right)}{f\left(x\right)}dx=ln|f\left(x\right)|+C$

Therefore, $\frac{1}{2}\int \frac{2cosx-3sinx}{3cosx+2sinx}=\frac{1}{2}ln|3cosx+2sinx|+C$