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Question
Mathematics
The integral 16 ∫ limits12 (d x/x3(x2+2)2) is equal to
Q. The integral
16
1
∫
2
x
3
(
x
2
+
2
)
2
d
x
is equal to
715
138
JEE Main
JEE Main 2023
Integrals
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A
6
11
−
lo
g
e
4
0%
B
12
11
+
lo
g
e
4
20%
C
6
11
+
lo
g
e
4
60%
D
12
11
−
lo
g
e
4
20%
Solution:
I
=
16
1
∫
2
x
3
(
x
2
+
2
)
2
d
x
=
16
1
∫
2
x
3
x
4
(
1
+
x
2
2
)
2
d
x
Let,
1
+
x
2
2
=
t
⇒
x
3
−
4
d
x
=
d
t
I
=
−
4
3
∫
2
3
(
t
−
1
2
)
2
t
2
d
t
I
=
−
4
3
∫
2
3
(
2
t
−
1
)
2
t
2
d
t
I
=
−
4
4
3
∫
2
3
(
1
−
t
2
+
t
2
1
)
d
t
I
=
−
1
[
t
−
2
ℓ
n
∣
t
∣
−
t
1
]
3
2
3
I
=
−
1
[
(
2
3
−
2
ℓ
n
2
3
−
3
2
)
−
(
3
−
2
ℓ
n
3
−
3
1
)
]
I
=
−
1
[
2
ℓ
n
2
−
6
11
]
I
=
6
11
−
ℓ
n
4