
Integration of Algebraic Rational Functions 13-21
and putting the numerators on the RHS over the same denominator, we get
x
x x
Ax B x x Cx D x E x
x( )( )
( )( )( ) ( )( ) ( )
( )(+ +
=
+ + + + + + + +
+1 1
1 1 1 1
1
2 2
2 2 2
xx
2 2
1+ )
.
Equating the numerators on both sides yields
( )( )( ) ( )( ) ( ) ( ).Ax B x x Cx D x E x x+ + + + + + + + =
2 2 2
1 1 1 1 Step 4
Comparing the coefficients of powers of x on both sides, we get
A B
A E
A B C E
+ + + =
+ =
+ =
+ + + =
0
0
2 0
and
+ + = 0 .
After solving the above system of equations with three unknowns, we get
A B C D E= = − = = = −
1
1
1
1
1
, , , , ( ).Step 6
Substituting the above values in Eq. ...