Consider the indefinite integral / cos (6t) sin(6t) dt. The most appropriate substitution to simplify this integral is u = Then du = E dt, so sin (6t) dt = c du, where the constant c = After making the substitution we obtain the integral / f(u) du, where f(u) = E This last integral, when evaluated, is After substituting back for u we obtain the following final form of the answer: cost2 (6t) sin(6t) dt =