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 =
= -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 * (1/7 * t^7 - 1/9 * t^9) + C = -1/21 * t^7 + 1/27 * t^9 + C =
= | t = cos (3x) | = -1/21 * cos^7 (3x) + 1/27 * cos^9 (3x) + C