PART 21：例題-快速分解(求不定積分)

\(\int {\frac{{2x + 1}}{{{x^2} - x - 6}}dx} \)

SOL：

\(\int {\frac{{2x + 1}}{{{x^2} - x - 6}}dx} \)  

\( = \int {\frac{{2x + 1}}{{(x - 3)(x + 2)}}dx} \)

\( = \int {\frac{{{\textstyle{7 \over 5}}}}{{(x - 3)}} + \frac{{{\textstyle{3 \over 5}}}}{{(x + 2)}}dx} \)  

\( = \frac{7}{5}\ln (x - 3) + \frac{3}{5}\ln (x + 2) + C\)