AP

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Evaluate ∫3x+5x2−4x+13 dx\displaystyle\int \frac{3x+5}{x^{2}-4x+13}\,dx. (a) 3ln⁡ ⁣(x2−4x+13)+113arctan⁡ ⁣(x−23)+C3\ln\!\left(x^{2}-4x+13\right)+\dfrac{11}{3}\arctan\!\left(\dfrac{x-2}{3}\right)+C (b) 32arctan⁡ ⁣(x−23)+113ln⁡ ⁣(x2−4x+13)+C\dfrac{3}{2}\arctan\!\left(\dfrac{x-2}{3}\right)+\dfrac{11}{3}\ln\!\left(x^{2}-4x+13\right)+C (c) 32ln⁡ ⁣(x2−4x+13)+11arctan⁡ ⁣(x−23)+C\dfrac{3}{2}\ln\!\left(x^{2}-4x+13\right)+11\arctan\!\left(\dfrac{x-2}{3}\right)+C (d) 32ln⁡ ⁣(x2−4x+13)+113arctan⁡ ⁣(x−23)+C\dfrac{3}{2}\ln\!\left(x^{2}-4x+13\right)+\dfrac{11}{3}\arctan\!\left(\dfrac{x-2}{3}\right)+C

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