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AP Calculus BC 6.10 Integrating Functions Using Long Division and Completing the Square Questions

Integrate rational expressions by polynomial division, algebraic rearrangement or completing the square before applying standard antiderivatives.

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.D—For integrands requiring substitution or rearrangements into equivalent forms: (a) Determine indefinite integrals. (b)…—Topic 6.10

Question 1

[Maximum number: 1]

∫−31x2+4x+5x−5dx=\int_{-3}^{1} \frac{x^{2}+4 x+5}{x-5} d x=

A

−59-\frac{5}{9}

B

983ln⁡2\frac{98}{3} \ln 2

C

-8

D

32-50 ln 2

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