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Byju's Answer
Standard XII
Mathematics
Special Integrals - 2
∫ e x [ x 3+ ...
Question
∫
e
x
[
x
3
+
x
+
1
(
1
+
x
2
)
3
/
2
]
d
x
is equal to
A
x
2
e
x
(
1
+
x
2
)
1
/
2
+
c
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B
e
x
x
(
1
+
x
2
)
1
/
2
+
c
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C
e
x
(
1
+
x
2
)
1
/
2
+
c
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D
x
e
x
(
1
+
x
2
)
1
/
2
+
c
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Solution
The correct option is
D
x
e
x
(
1
+
x
2
)
1
/
2
+
c
I
=
∫
e
x
[
x
√
1
+
x
2
+
1
(
1
+
x
2
)
3
/
2
]
d
x
Let
f
(
x
)
=
x
√
1
+
x
2
⇒
f
′
(
x
)
=
√
1
+
x
2
−
x
2
√
1
+
x
2
(
1
+
x
2
)
=
1
(
1
+
x
2
)
3
/
2
∴
I
=
e
x
f
(
x
)
+
c
=
e
x
x
√
1
+
x
2
+
c
Suggest Corrections
20
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d
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l
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