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AP Calculus AB 6.8 Antiderivatives and Indefinite Integrals Question Bank

Practise antiderivative questions by reversing derivative rules, using indefinite-integral notation and including the constant of integration.

Syllabus
Effective Fall 2025
Course
AP Calculus AB

Exam points

  • determine antiderivatives by reversing known derivative rules
  • write indefinite integrals with a correct constant of integration

FUN-6.C—Determine antiderivatives of functions and indefinite integrals, using knowledge of derivatives question 1

[Maximum number: 1]

∫(12x+2x)dx=\int\left(\frac{1}{2 x}+2^{x}\right) d x=

A

−12x2+2xln⁡2+C-\frac{1}{2 x^{2}}+2^{x} \ln 2+C

B

12ln⁡∣x∣+2x+1x+1+C\frac{1}{2} \ln |x|+\frac{2^{x+1}}{x+1}+C

C

12ln⁡∣x∣+2xln⁡2+C\frac{1}{2} \ln |x|+\frac{2^{x}}{\ln 2}+C

D

ln⁡∣2x∣+2xln⁡2+C\ln |2 x|+\frac{2^{x}}{\ln 2}+C

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