# Integration of Rational Fractions | Techniques of Integration

## Partial Fractions

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 $P(x)$ is less in degree power than $Q(x)$. 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 $(x - 4) / (2x^2 - 4x)$ can be expressed as the sum of **partial fractions**, 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.

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