Consider the indefinite integral / cos (3t) sin(3t) dt. The most appropriate substitution to simplify this integral is u = cos(3t) Then du = -3sin(3t) E dt, so sin (3t) dt = c du, where the constant c = -1/3 After making the substitution we obtain the integral / f(u) du, where f(u) = -U^13/39+C This last integral, when evaluated, is -Cos^ 13(3t)/39+C E After substituting back for u we obtain the following final form of the answer: cost3 (3t) sin(3t) dt = -cos^13(3t)/39+C