$\int \frac{(2 x + 1)}{(x + 2) (x - 3)} d x$

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Solution

$\int \frac{2 x + 1}{(x + 2) (x - 3)} d x$

$= \int [\frac{3}{5 (x + 2)} + \frac{7}{5 (x - 3)}] d x$

$= \frac{3}{5} \int \frac{d x}{x + 2} + \frac{7}{5} \int \frac{d x}{x - 3}$

$= \frac{3}{5} log (x + 2) + \frac{7}{5} log (x - 3) + c$

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