A Level

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

Problem

Evaluate ∫tan⁡−1(2x) dx\displaystyle\int \tan^{-1}(2x) \, dx. (a) xtan⁡−1(2x)+14ln⁡(1+4x2)+Cx\tan^{-1}(2x) + \dfrac{1}{4}\ln(1+4x^{2}) + C (b) xtan⁡−1(2x)−12ln⁡(1+4x2)+Cx\tan^{-1}(2x) - \dfrac{1}{2}\ln(1+4x^{2}) + C (c) xtan⁡−1(2x)−14ln⁡(1+4x2)+Cx\tan^{-1}(2x) - \dfrac{1}{4}\ln(1+4x^{2}) + C (d) x2tan⁡−1(2x)−14ln⁡(1+4x2)+C\dfrac{x}{2}\tan^{-1}(2x) - \dfrac{1}{4}\ln(1+4x^{2}) + C

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