Integration Using Partial Fractions
( i ) If f ( x ) and g ( x ) are two polynomials , then f ( x ) / g ( x ) defines a rational algebraic function of x . If degree of f ( x ) < degree of g ( x ), then f ( x ) / g ( x ) is called a proper rational function .
( ii ) If degree of f ( x ) ≥ degree of g ( x ), then f ( x ) / g ( x ) is called an improper g ( x ) rational function .
( iii ) If f ( x ) / g ( x ) isan improper rational function , then we divide f ( x ) by g ( x ) g ( x ) and convert it into a proper rational function as f ( x ) / g ( x ) = φ ( x ) + h ( x ) / g ( x ).
( iv ) Any proper rational function f ( x ) / g ( x ) can be expressed as the sum of rational functions each having a simple factor of g ( x ). Each such fraction is called a partial fraction and the process of obtaining them , is called the resolution or decomposition of f ( x ) / g ( x ) partial fraction .