AP Calculus AB: u-Substitution — Drill 1

About This Drill

AP Calculus AB: u-Substitution — Drill 1 is a Math practice drill covering u-Substitution. It contains 5 original questions created by Brian Stewart, a Barron's test prep author with over 20 years of tutoring experience.

Practice u-substitution for both indefinite and definite integrals, including recognizing the correct substitution, changing bounds, and working with trigonometric and exponential functions. These AP Calculus AB integration skills are tested on both the multiple-choice and free-response sections.

Questions in This Drill

1. Let \( u = x^2 + 1 \). What is \( \int 2x(x^2 + 1)^4 \, dx \)?
2. What is \( \int_0^1 x \, e^{x^2} \, dx \)?
3. What is \( \int \cos(3x) \, dx \)?
4. A student evaluates \( \int_0^2 x^2 e^{x^3} \, dx \) using the substitution \( u = x^3 \). Which of the following correctly shows the integral after substituting and changing the bounds?
5. Which of the following integrals can both be evaluated using u-substitution with \( u = \ln x \)?
   
   (I)  \( \int \dfrac{\ln x}{x} \, dx \)     (II)  \( \int \dfrac{1}{x \ln x} \, dx \)     (III)  \( \int x \ln x \, dx \)