2
2
( – ) (
)
px
qx
r
x
a
x – b
+
+
2
A
B
C
(
)
x – a
x – b
+x – a
+
5 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