$\int \frac{x + 7}{3 x^{2} + 25 x + 28} d x$

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Solution

$I = \int \frac{x + 7}{3 x^{2} + 25 x + 28} d x = \int \frac{x + 7}{3 x^{2} + 21 x + 4 x + 28} d x = \int \frac{x + 7}{3 x (x + 7) + 4 (x + 7)} d x = \int \frac{x + 7}{(3 x + 4) (x + 7)} d x$

$= \int \frac{1}{(3 x + 4)} d x = \frac{1}{3} \ln |3 x + 4| + c$

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