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AP Calculus AB 6.9 Integration by Substitution Question Bank

Practise substitution-integration questions by choosing a new variable, changing the differential and simplifying the resulting integral.

Syllabus
Effective Fall 2025
Course
AP Calculus AB

Exam points

  • choose a substitution that simplifies the integrand and differential
  • rewrite bounds or back-substitute and evaluate the integral correctly

FUN-6.D—For integrands requiring substitution or rearrangements into equivalent forms: (a) Determine indefinite integrals. (b) Evaluate… question 1

[Maximum number: 1]

∫01xx2+1dx\int_{0}^{1} \frac{x}{x^{2}+1} d x is equal to

A

π4\frac{\pi}{4}

B

ln⁡2\ln \sqrt{2}

C

12(ln⁡2−1)\frac{1}{2}(\ln 2-1)

D

ln⁡2\ln 2

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