Evaluate: $\int \frac{\sin 2x}{\sin 5x\sin 3x}dx$

The correct option is A $\frac{1}{3}\ln |\sin 3x|-\frac{1}{5}\ln |\sin 5x|+C$

$I=\int \left(\frac{sin(5x-3x)}{sin5xsin3x}\right)dx$

$I=\int \left(\frac{sin5x\cos 3x-cos5x\sin 3x}{sin5xsin3x}\right)dx$

$I=\int \left(\frac{cos3x}{sin3x}\right)dx-\int \left(\frac{cos5x}{sin5x}\right)dx$

$I=\left(\frac{1}{3}\right)log|sin3x|-\left(\frac{1}{5}\right)log|sin5x|+c$