Integration by Partial Fractions/Examples/Arbitrary Example 1

Example of Use of Integration by Partial Fractions
Let $\map R x = \dfrac {\map P x} {\map Q x}$ be a rational function over $\R$ such that the degree of the polynomial $P$ is strictly smaller than the degree of the polynomial $Q$.

Let $\map Q x$ be expressible as:
 * $\map Q x = \paren {x - a} \paren {x - b}^2 \paren {x^2 + c x + d}$

Then:

where $A$, $B_1$, $B_2$, $C$ and $D$ are constants dependent upon $a$, $b$, $c$ and $d$.