Consider the indefinite integral ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{5x^{3}5x^2-40x-54}{x^2-9}dx$

Then the integrand decomposes into the form

Integrating term by term, we obtain that

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{5x^{3}5x^2-40x-54}{x^2-9}dx=$