Was ist das Integral von `sin ^ 5 (x) * cos ^ 3 (x)`?

`int sin^5 x*cos ^3 x d x=?`

`int sin^5 x* cos^2x *cos x d x`

`cos^2 x=1-sin^2 x`

`int sin^5 x(1-sin^2 x) cos x d x`

`int (sin^5x-sin^7x)cos x d x`

`sin x=u" ; " cos x d x=d u`

`int (u^5-u^7)d u`

`int sin^5 x*cos ^3 x d x=1/6 u^6-1/8 u^8 +C`

`int sin^5 x*cos ^3 x d x=1/6sin^6 x-1/8 sin^8 x+C`