Evaluate $\int \frac{3 x}{2 x^{2} + 5} d x$

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Solution

$\int \frac{3 x}{2 x^{2} + 5} d x t = 2 x^{2} + 5 ⟹ 4 x d x = d t \int \frac{3}{4} \frac{1}{t} d t \frac{3}{4} log t \frac{3}{4} log (2 x^{2} + 5) + c$

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