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Question
Mathematics
∫ ((x2+1) ex/(x+1)2) d x=f(x) ex+C, Where C is a constant, then (d3 f/d x3) at x =1 is equal to :
Q.
∫
(
x
+
1
)
2
(
x
2
+
1
)
e
x
d
x
=
f
(
x
)
e
x
+
C
, Where
C
is a constant, then
d
x
3
d
3
f
at
x
=
1
is equal to :
982
177
JEE Main
JEE Main 2022
Integrals
Report Error
A
−
4
3
29%
B
4
3
14%
C
−
2
3
57%
D
2
3
0%
Solution:
∫
(
(
x
+
1
)
2
x
2
+
1
)
e
x
⋅
d
x
=
∫
(
(
x
+
1
)
2
x
2
−
1
+
2
)
e
x
d
x
=
∫
(
x
+
1
x
−
1
+
(
x
+
1
)
2
2
)
e
x
d
x
=
∫
(
f
(
x
)
+
f
′
(
x
)
)
e
x
d
x
=
f
(
x
)
e
x
+
c
Where
f
(
x
)
=
x
+
1
x
−
1
f
′
(
x
)
=
(
x
+
1
)
2
2
f
′′
(
x
)
=
(
x
+
1
)
3
−
4
=
(
x
+
1
)
4
12
f
′′
(
1
)
=
16
12
=
4
3