® Integration by partial fractions

® Integration by partial fractions Recall that a rational function is ratio of two polynomials of the form P( ) Q( ) x , where P( x ) and Q ( x ) are polynomials in x and Q ( x ) ≠ . If degree of the polynomial P ( x ) is greater than the degree of the polynomial Q ( x ), then we may divide P ( x ) by Q ( x ) so that P ( ) P( ) T ( ) Q( ) Q( ) , where T( x ) is a polynomial in x and degree of P ( x ) is less than the degree of Q( x ). T( x ) being polynomial can be easily integrated. P ( ) Q( ) x can be integrated by expressing P ( ) Q( ) x as the sum of partial fractions of the following type: . ) ( px q A B , a ≠ b . px q A B INTEGRALS . ) ( ) ( px qx r A B . ) ( px qx r A B . ) ( px qx r bx A B + C bx where x + bx + c can not be factorised further.