4 THE SUBSTITUTION RULE If u g x is a differentiable

Last updated: 12/15/2023

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 f g x g x dx f f u du EXAMPLE I Find x cos x 2 dx u x 2 so du 4x dx x dx du 4 x cos x 2 dx cos u du cos u du sin u C sin x4 2 C 8 x x 5 dx 10 3 2 4 dt C