Question

Integrate: $f\left(x\right)=\frac{{\sin }^{3}x+{\cos }^{3}x}{{\sin }^{2}x{\cos }^{2}x}$

Answer 1

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

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

$=\int \sec x\tan xdx+\int \csc x\cot xdx$

$=\sec x-\csc x+c$ (Ans)