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\newcommand\ds{\displaystyle}

\begin{document}

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QUESTION

Evaluate $\ds\int_0^1\frac{1}{2x+1}\,dx$.

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ANSWER

$\ds\int_0^1\frac{1}{2x+1}\,dx
=\left[\frac{1}{2}\ln(2x+1)\right]_0^1
=\frac{1}{2}\ln3-\frac{1}{2}\ln1=\frac{1}{2}\ln3$


\end{document}