Интеграл от cos^3 x *sin 2x по dx

Question

Интеграл от cos^3 x *sin 2x по dx

Answer 1

cos^3 x *sin 2x=2cos^3 x*cos x*sin x=2cos^4 x *sin x

Integral 2cos^4 x *sin x dx=

= 2 integral sin(x) cos^4(x) dx

t = cos(x) , dt = -sin(x) dx:

= -2 integral t^4 dt

= -(2 t^5)/5+C

t = cos(x):

= -2/5 cos^5(x)+C