Consider the indefinite integral [164(6 + 11x5)6 dx. The most appropriate substitution to simplify this integral is u = 2 Then du = 2 dx (fill in the blank with a suitable constant or function of x), and so x4 dx = c du, for the constant c = 2 After making these substitutions we obtain the integral / f (u) du, where f (u) = This last integral, when evaluated, is 2 After substituting back for u we obtain the following final form of the answer: [x4(6+11x5)6dx= z 6 x Consider the indefinite integral / dx. V 5 + 12x7 The most appropriate substitution to simplify this integral is u = 2 Then du = 2 dx (fill in the blank with a suitable constant or function of x), and so x6 dx = c du, for the constant c = 2 After making the substitution we obtain the integral / f(u) du, where f (u) = Z This last integral, when evaluated, is 2 After substituting back for u we obtain the following final form of the answer: 6 /x_dx: z W 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 = E After making the substitution we obtain the integral f(u) du, where f(u) = This last integral, when evaluated, is After substituting back for u we obtain the following final form of the answer: cost (6t) sin(61) dt =