8.0 Integration using partial fractions

8.1 Type A: Linear and non-repeating
8.2 Type B: Linear and repeating
8.3 Type C: Quadratic and non-repeating
8.4 Type D: Quadratic and repeating

Let us assume $f(x)$ and $g(x)$ be two polynomials and to find the integral of the type $$\frac{{f(x)}}{{g(x)}}$$ which is a rational algebraic function of $x$ following two cases are there:

Case I: When degree of $f(x)$ is less than degree of $g(x)$ then $\frac{{f(x)}}{{g(x)}}$ is called proper rational function which is expressed as the sum of rational functions and solved using partial fractions.

The partial fractions depends on the nature of the factors of denominator $g(x)$ due to which the following different types are there when the factors of $g(x)$ are: