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AP Calculus BC 6.8 Antiderivatives Overview

Reverse familiar derivative rules to find indefinite integrals, simplify integrands and include the constant of integration.

Syllabus
Effective Fall 2025
Course
AP Calculus BC

Exam points

  • identify the governing calculus relationship in the problem
  • justify the result with symbolic, graphical or contextual evidence

Covered syllabus points

FUN-6.C—Determine antiderivatives of functions and indefinite integrals, using knowledge of derivatives

6.8 Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation question 1

[Maximum number: 1]

∫1ttdt=\int \frac{1}{t \sqrt{t}} d t=

A

−2t−1/2+C-2 t^{-1 / 2}+C

B

−32t−5/2+C-\frac{3}{2} t^{-5 / 2}+C

C

−25t−5/2+C-\frac{2}{5} t^{-5 / 2}+C

D

2t1/2ln⁡t+C2 t^{1 / 2} \ln t+C

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