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AP EAMCET Engineering 2015 Code C Paper
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Question : 39
Total: 160
∫
x
+
1
x
(
1
+
x
e
x
)
d
x
=
log
|
1
+
x
e
x
x
e
x
|
+
C
log
|
x
e
x
1
+
x
e
x
|
+
C
e
x
(
x
−
1
x
+
1
)
+
C
e
x
(
x
+
1
x
−
1
)
+
C
Validate
Solution:
∫
x
+
1
x
(
1
+
x
e
x
)
d
x
=
∫
e
x
(
x
+
1
)
x
e
x
(
1
+
x
e
x
)
d
x
x
e
x
=
t
=
∫
d
t
t
(
1
+
t
)
=
∫
(
1
t
−
1
1
+
t
)
d
t
=
log
(
t
1
+
t
)
+
C
=
log
(
x
e
x
1
+
x
e
x
)
+
C
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