int sin^3 (3x) * cos^6 (3x) dx = int sin^2 (3x) * cos^6 (3x) * sin (3x) dx =
= int (1 - cos^2 (3x)) * cos^6 (3x) * sin (3x) dx =
= int (1 - cos^2 (3x)) * cos^6 (3x) d(-cos (3x)/3) =
= -1/3 * int (1 - cos^2 (3x)) * cos^6 (3x) d(cos (3x)) = | t = cos 3x | =
= -1/3 * int (1 - t^2) * t^6 dt = -1/3 * int (t^6 - t^8) dt =
= -1/3 * (t^7/7 - t^9/9) + C = t^9/27 - t^7/21 + C = | t = cos 3x | =
= cos^9 (3x)/27 - cos^7 (3x)/21 + C