Question

Неопределенный интеграл sin^2 x cos x dx

Answer 1

$int {sin^2xcosx} , dx =int{(1-cos^2x)cosx,dx}=int (cosx-cos^3x) dx=\\=int cosxdx-int cos^3xdx= left[begin{array}{ccc}cosx=t, dx=dtend{array}right] =sinx-int t^3dt=\\=sinx-frac{t^4}{4}+C=sinx-frac{cos^4x}{4}+C.$