Question

Интеграл sin^5x/cos^2x

Answer 1

$\int\frac{sin^5x}{cos^2x}dx=\int\frac{sinx(1-cos^2x)^2}{cos^2x}=-\int\frac{1-2cos^2+cos^4x}{cos^2x}d(cosx)=\\=-\int(cos^2x-2+\frac{1}{cos^2x})d(cosx)=-\frac{cos^3x}{3}+2cosx+\frac{1}{cosx}+C$