Answer:
Let, I=∫
1/2
(an−1)/n
a−x
+
x
dx
=∫
n
1
a−
dx ....(i)
a−(
+a−
−x)
−x
(
)
⇒I=∫
dx .... (ii)
On adding Eqs. (i) and (ii), we get
2I=∫
1dx=[x]
=a−
−
=
na−2
⇒I=
2n
.
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Verified answer
Answer:
Let, I=∫
1/2
(an−1)/n
a−x
+
x
x
dx
=∫
n
1
a−
n
1
a−x
+
x
x
dx ....(i)
=∫
n
1
a−
n
1
a−(
n
1
+a−
n
1
−x)
+
n
1
+a−
n
1
−x
(
n
1
+a−
n
1
−x
)
dx
⇒I=∫
n
1
a−
n
1
x
+
a−x
a−x
dx .... (ii)
On adding Eqs. (i) and (ii), we get
2I=∫
n
1
a−
n
1
1dx=[x]
n
1
a−
n
1
=a−
n
1
−
n
1
=
n
na−2
⇒I=
2n
na−2
.