Evaluate $\int \frac{2 x}{x^{2} + 1} d x$ .

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Solution

$I = \int \frac{2 x}{x^{2} + 1} d x$

Let $x^{2} + 1 = t$

$2 x d x = d t$

Therefore, $I = \int \frac{d t}{t} = log t + C$

$I = log | x^{2} + 1 | + C$

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