Интеграл от cos^3 x * sin 2x по dx

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