5.∫ x (2 + x) dx
6.∫ (x^3 + x)^2 dx
7.
8.∫ x(x − 1)^3 dx
9.∫ sec x(sec x + tan x) dx
10.∫ (sec^2 x + x) dx
11.
12.
13.∫ (1 + cos^2 x sec x) dx
14.
15.
u-SUBSTITUTION
When we discussed differentiation, one of the most important techniques we mastered was the Chain
Rule. Now, you’ll learn the integration corollary of the Chain Rule (called u-substitution), which we use
when the integrand is a composite function. All you do is replace the function with u, and then you can
integrate the simpler function using the Power Rule (as shown below).