Question

Solve $\int \frac{6{\sin }^{3}x+5{\cos }^{3}x}{{\sin }^{2}x{\cos }^{2}x}dx$

Answer 1

Given that:

$=\int \frac{6{\sin }^{3}x+5{\cos }^{3}x}{{\sin }^{2}x{\cos }^{2}x}dx$

$=\int \frac{6\sin x}{{\cos }^{2}x}dx+\int \frac{5\cos x}{{\sin }^{2}x}dx$

$=\int 6\tan x\sec xdx+\int 5\cot x\csc xdx$

$[\because \int \tan x\sec x=\sec x,\int \cot x\csc xdx=-\csc x]$

$=6\sec x+5(-\csc x)+constant$

$=6\sec x-5\csc x+constant$