Consider the indefinite integral ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{x^2}{(x-6)(x-7{)}^2}dx$ Then the integrand has partial fractions decomposition

$\frac{a}{x-6}\frac{b}{x-7}\frac{c}{(x-7{)}^2}$

where

$a=36$

$b=-35$

$c=49$

Integrating term $by$ term, $we$ obtain that

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{x^2}{(x-6)(x-7{)}^2}dx=$

$36ln(|x-6|)-35ln((|x-7|)-\frac{49}{x-7})C$