(a)[3]
If $2x = \tan y$, prove that $\frac{dy}{dx} = \frac{2}{1 + 4x^2}$.
(b)[7]
Hence determine the exact value of $\int_{\frac{1}{2}}^{\frac{\sqrt{3}}{2}} x\tan^{-1}(2x)\,dx$.
Mathematics 9709 · AS & A Level · Integration
Integration — practice question
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