$(10\mathrm{.}01,10\mathrm{.}02,10\mathrm{.}03HC)$

Let $f$ be the function defined by $f(x)=\frac{7}{2x^2+x-6}.$

Part A: Use partial fractions to evaluate ${\displaystyle \underset{3}{\overset{}{}}}f(x)dx,$ or show that the integral diverges. $(7$ points$)$

Part B: Determine whether the series ${\displaystyle \underset{k=3}{\overset{}{}}}\frac{7}{2k^2+k-6}$ converges or diverges. State the conditions used for determining convergence or divergence. $(3$ points$)$