Partial Fraction Decomposition
The procedure of taking a rational expression and splitting down it into simpler rational expressions which we can add or subtract to get the original rational expression is termed as partial fraction decomposition. Several integrals including rational expressions can be completed if we first do partial fractions on the integrand.
Thus, let's do a quick review of partial fractions. We will begin with a rational expression in the form,
f (x) = P(x) / Q (x)
In which both P(x) and Q(x) are polynomials and the degree of P(x) is smaller as compared the degree of Q(x). Again call that the degree of a polynomial is the largest exponent in the polynomial. Partial fractions can just only be completed if the degree of the numerator is strictly less as compared to the degree of the denominator. That is vital to remember.
Thus, once we've ascertained that partial fractions can be done we issue the denominator as completely as possible. After that for every factor in the denominator we can make use of the following table to ascertain the term(s) we pick up in the partial fraction decomposition.