AP Calculus AB: Antiderivatives and Basic Integration Rules — Drill 1

About This Drill

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

Practice finding antiderivatives using the power rule, standard integral formulas for exponential, logarithmic, and trigonometric functions, and solving initial value problems. These are foundational integration skills for the AP Calculus AB exam.

Questions in This Drill

1. What is \( \int (4x^3 - 6x + 5)\,dx \)?
2. What is \( \int \left( e^x + \dfrac{3}{x} \right) dx \)?
3. Which of the following is an antiderivative of \( f(x) = \sec^2 x - \sin x \)?
4. If \( F'(x) = 3x^2 - 4x \) and \( F(1) = 5 \), what is \( F(x) \)?
5. A student claims that \( \int (2x + 1)\,dx = x^2 + x \) is a complete and valid answer. Which of the following best describes the error?