Integrate $\displaystyle \int\frac{{{x}^{{2}}-{x}+{6}}}{{{x}^{{3}}+{3}{x}}}{\left.{d}{x}\right.}$.

The partial fraction decomposition is (write all terms as fractions):

$\displaystyle \int$ dx Preview Question 6 Part 1 of 2  

The final answer is:

$\displaystyle \int\frac{{{x}^{{2}}-{x}+{6}}}{{{x}^{{3}}+{3}{x}}}{\left.{d}{x}\right.}=$ Preview Question 6 Part 2 of 2