Determine an antiderivative of .

MATHEMATICS · Single correct · A Level · Mathematics · Integration · Integration

Problem

Determine an antiderivative of 14x2−4x+5\displaystyle\frac{1}{4x^{2}-4x+5}. (a) 12ln⁡∣4x2−4x+5∣+C\dfrac{1}{2}\ln\left|4x^{2}-4x+5\right|+C (b) 14arctan⁡(x−12)+C\dfrac{1}{4}\arctan\left(x-\dfrac{1}{2}\right)+C (c) arctan⁡(x−12)+C\arctan\left(x-\dfrac{1}{2}\right)+C (d) 12arctan⁡(2x−1)+C\dfrac{1}{2}\arctan\left(2x-1\right)+C

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