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Question
Solution
\[Let I = \int_2^3 \frac{x}{x^2 + 1} d x . Then, \]
\[I = \frac{1}{2} \int_2^3 \frac{2x}{x^2 + 1}\]
\[ \Rightarrow I = \frac{1}{2} \left[ \log \left( x^2 + 1 \right) \right]_2^3 \]
\[ \Rightarrow I = \frac{1}{2}\left( \log 10 - \log 5 \right)\]
\[ \Rightarrow I = \frac{1}{2}\log \frac{10}{5} \left[ \because \log a - \log b = \log \frac{a}{b} \right]\]
\[ \Rightarrow I = \frac{1}{2}\log 2\]
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