AP Calculus BC 6.10 Long Division & Completing the Square

Practise AP Calculus BC 6.10 by rearranging rational integrands with polynomial long division or completing the square before evaluating indefinite and definite integrals.

Exam points

Use polynomial long division to rewrite rational integrands before integrating polynomial and logarithmic terms.
Complete the square in quadratic denominators to recognise arctangent antiderivatives.

[Maximum number: 1]

$\int_{-3}^{1} \frac{x^{2}+4 x+5}{x-5} d x=$

$-\frac{5}{9}$

$\frac{98}{3} \ln 2$

-8

32-50 ln 2

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FUN-6.D—For integrands requiring substitution or rearrangements into equivalent forms: (a) Determine indefinite integrals. (b)…—Topic 6.10 question 1