Ta có:
$\int\dfrac{\cos^5x}{1-\sin x}dx$
$=\int\dfrac{\cos^4x}{1-\sin x}d(\sin x)$
$=\int\dfrac{(1-\sin^2x)^2}{1-\sin x}d(\sin x)$
$=\int[(1+\sin x)(1-\sin^2x)]d(\sin x)$
$=\int(1+\sin x-\sin^2x-\sin^3x)d(\sin x)$
$=\sin x+\dfrac{\sin^2x}{2}-\dfrac{\sin^3x}{3}-\dfrac{\sin^4x}{4}+C$