A Level

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

Problem

Evaluate ∫01arctan⁡(2x) dx\displaystyle\int_{0}^{1}\arctan(2x)\,dx. (a) arctan⁡2  −  12ln⁡5\arctan 2\; -\; \dfrac{1}{2}\ln 5 (b) arctan⁡2  −  14ln⁡5\arctan 2\; -\; \dfrac{1}{4}\ln 5 (c) arctan⁡2  +  14ln⁡5\arctan 2\; +\; \dfrac{1}{4}\ln 5 (d) arctan⁡2  −  18ln⁡5\arctan 2\; -\; \dfrac{1}{8}\ln 5

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