4 THE SUBSTITUTION RULE If u = g(x) is a differentiable function whose range is an interval I and f is continuous on I, then f (g(x))g'(x) dx = f(u) du EXAMPLE I Find ( x cos(x4 + 2) dx. u = x + 2 SO du = 4x dx, x dx = du/4 S x cos(x4 + 2) dx = cos u / du = cos u du = sin u + C =sin(x4 + 2) + C 8. x ( + 5) dx [ (3+ + 2).4 dt. 10. (3t