Evaluate: _1^2 x 1+x^2 d x - Vidyadip

Question

Evaluate: $\int_1^2 \frac{x}{1+x^2} d x$

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Answer

$\int_1^2 \frac{x}{1+x^2} d x=\frac{1}{2} \int_1^2 \frac{2 x}{1+x^2} d x$
$=\frac{1}{2}\left[\log \left|1+x^2\right|\right]_1^2 \quad \ldots \ldots . . .\left[\frac{ f ^{\prime}(x)}{ f (x)} d x=\log | f (x)|+c\right]$
$=\frac{1}{2}(\log 5-\log 2)$
$=\frac{1}{2} \log \left(\frac{5}{2}\right)$

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