Question

Evaluate :

$\int \frac{2\cos x}{3{\sin }^{2}x}dx$

Answer 1

$I=\int \frac{2\cos x}{3{\sin }^{2}x}dx$

Let $\sin x=t⟹\cos xdx=dt$

Therefore, $I=\int \frac{2dt}{3t^2}$

$I=\frac{2}{3}\frac{t^{-1}}{(-1)}$

$I=-\frac{2}{3}(\sin x{)}^{-1}+C$