Question

Интеграл sin^5x/cos^2x

Answer 1

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