$(4$ pts$)$ For this integral, partial fraction decomposition has already been performed and the integral has already been rewritten. Integrate each term of this result.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(\frac{2}{x+6}-\frac{3}{(x+7{)}^2}+\frac{4x}{x^2+8}+\frac{5}{x^2+9})dx$