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Tardigrade
Question
Mathematics
The value of ∫ ( ln ((x-1/x+1))/x2-1) d x is equal to
Q. The value of
∫
x
2
−
1
l
n
(
x
+
1
x
−
1
)
d
x
is equal to
328
160
Integrals
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A
2
1
ℓ
n
2
x
+
1
x
−
1
+
C
B
4
1
ln
2
x
+
1
x
−
1
+
C
C
2
1
ℓ
n
2
x
−
1
x
+
1
+
C
D
4
1
ℓ
n
2
x
−
1
x
+
1
+
C
Solution:
I
=
∫
x
2
−
1
l
n
(
x
+
1
x
−
1
)
d
x
put
ln
(
x
+
1
x
−
1
)
=
t
⇒
x
2
−
1
2
d
x
=
d
t
⇒
I
=
∫
t
2
d
t
=
4
t
2
+
C
=
lo
g
2
(
x
+
1
x
−
1
)
+
C
=
4
1
lo
g
2
(
x
−
1
x
+
1
)
+
C