\(\int \frac{dx}{3x^{2}+13x-10}\) equals

\(\frac{1}{17}\log \left|\frac{3x-2}{x+5}\right|+C\)

\(\int \frac{dx}{3x^{2}+13x-10}\)

$=\frac{1}{3}\int\frac{dx}{(x+\frac{13}{6})^2-(\frac{17}{6})^2}$

$=\frac{1}{3×2}×\frac{6}{17}\log\left|\frac{x+\frac{13}{6}-\frac{17}{6}}{x+\frac{13}{6}+\frac{17}{6}}\right|+C$

$=\frac{1}{17}\log\left|\frac{3x-2}{x+5}\right|+C$