(1)
where, real numbers A and B are to be determined suitably This gives
1 = A (x + 2) + B (x + 1) Equating the coefficients of x and the constant term, we get
A + B = 0
and
2A + B = 1
Solving these equations, we get A =1 and B = – 1 Thus, the integrand is given by
1
(
1) (
2)
x
x
+
+
 =
1
–1
1
2
x
x
+
+
+
Therefore,
(
1) (
2)
dx
x
x
+
+
∫
 =
1
2
dx
dx
–
x
x
+
+
∫
∫
= log
1
log
2
C
x
x
+
−
+
+
=
1
log
C
2
xx
+
+
+
Remark The equation (1) above is an identity, i