Question

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

Answer 1

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

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

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

$=\int \sec x\mathrm{tanx}dx+\int \cos ecxdx$

$=\sec x+\log \left|\cos ecx-\cot x\right|+c$