Question

∫▒〖cos2x/cosxsinx dx〗

Answer 1

$\int \frac{cos2x}{cosx\cdot sinx}dx=\int \frac{cos2x}{\frac{1}{2}sin2x}dx=[\, t=sin2x, \; dt=2cos2x\, dx\, ]=\\\\=\int\; \frac{dt}{t}=ln |t|+C=ln|sin2x|+C$