# Integration of Rational Fractions | Techniques of Integration

## Partial Fraction

Functions of x that can be expressed in the form P(x)/Q(x), where both P(x) and Q(x) are polynomials of x, is known as **rational fraction**. A rational fraction is known to be a **proper fraction** if the degree of P(x) is less than the degree of Q(x). Example of proper fraction is...

A rational fraction is said to be an improper fraction if the degree of P(x) is greater than or equal to the degree of Q(x). Examples are...

Improper fraction may be expressed as the sum of a polynomial and a proper fraction. For example:

Proper fraction such as $\,\, \dfrac{x - 4}{2x^2 - 4x} \,\,$ can be expressed as the sum of **partial fraction**, provided that the denominator will *factorized*.

Integration of any rational fraction depends essentially on the integration of a proper fraction by expressing it into a sum of partial fractions. There are four cases that may arise in dealing with integrand involving proper fraction.