Question

помогите решить интеграл   
$\int\limits sin^5xcos^4x,dx$

Answer 1

$\displaystyle \int sin^5xcos^4xdx=\int sinx*(1-cos^2x)^2*cos^4x\ dx=\\=-\int(1-2cos^2x+cos^4x)*cos^4x\ d(cosx)=\\-\int (cos^4x-2cos^6x+cos^8x)d(cosx)=\\=-\frac{cos^5x}{5}+\frac{2cos^7x}{7}-\frac{cos^9x}{9}+C$