2
2
( –
) (
)
px
qx
r
x
a
x
bx
c
+
+
+
+
2
A
B + C
x
x – a
x
bx
c
+
+
+
,
where x2 + bx + c cannot be factorised further
In the above table, A, B and C are real numbers to be determined suitably 318
MATHEMATICS
Example 11 Find 
(
1) (
2)
dx
x
x
+
+
∫
Solution The integrand is a proper rational function Therefore, by using the form of
partial fraction [Table 7 2 (i)], we write
1
(
1) (
2)
x
x
+
+
 =
A
B
1
2
x
x
+
+
+