Algebraic fractions can be integrated by separating into partial fractions and integrated using the standard result:

\(\displaystyle\int{\dfrac{1}{x}} dx = \ln{x} + c \)

For example:

\(\displaystyle\int{\dfrac{px+q}{(x+a)(x+b)}} dx = \displaystyle\int{\bigg(\dfrac{A}{x+a}+\dfrac{B}{x+b}\bigg)} dx \)

\(\quad = A\ln{|x+a|} + B\ln{|x+b|} + c \)