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AP Calculus BC/Unit 6: Integration and Accumulation of Change
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Integrating an Improper Rational Function

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Which of the following is an antiderivative of 4x2−4x+5x2−2x+2\frac{4x^2 - 4x + 5}{x^2 - 2x + 2}?

A

4x+3ln⁡∣x−1∣+2arctan⁡(x−1)+C4x + 3\ln|x-1| + 2\arctan(x-1) + C

B

2x2−4x+5ln⁡∣x−1∣+C2x^2 - 4x + 5\ln|x-1| + C

C

4x+3ln⁡∣x2−2x+2∣−2arctan⁡(x−1)+C4x + 3\ln|x^2-2x+2| - 2\arctan(x-1) + C

D

4x+2ln⁡∣x2−2x+2∣+arctan⁡(x−1)+C4x + 2\ln|x^2-2x+2| + \arctan(x-1) + C

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