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Question
Mathematics
∫ exloga ex dx is equal to
Q.
∫
e
x
l
o
g
a
e
x
d
x
is equal to
4612
197
AMU
AMU 2010
Integrals
Report Error
A
(
a
e
)
x
+
C
12%
B
l
o
g
(
a
e
)
(
a
e
)
x
+
C
44%
C
1
+
l
o
g
a
(
e
)
x
+
C
28%
D
N
o
n
e
o
f
t
h
ese
15%
Solution:
∫
e
x
l
o
g
a
e
x
d
x
I
=
∫
a
x
⋅
e
x
d
x
…
(
i
)
⇒
I
=
[
e
x
⋅
l
o
g
e
a
a
x
−
∫
e
x
⋅
l
o
g
e
a
a
x
d
x
]
⇒
I
=
l
o
g
e
a
e
x
⋅
a
x
−
l
o
g
e
a
1
∫
e
x
⋅
a
x
⋅
d
x
⇒
I
=
l
o
g
e
a
e
x
⋅
a
x
−
l
o
g
e
a
1
∫
e
x
⋅
a
x
⋅
d
x
⇒
I
=
l
o
g
e
a
e
x
⋅
a
x
−
l
o
g
e
a
1
⋅
I
[from Eq.t(i)]
⇒
(
l
o
g
e
a
1
+
l
o
g
e
a
)
I
=
l
o
g
e
a
e
x
⋅
a
x
⇒
(
l
o
g
e
e
+
l
o
g
e
a
)
I
=
e
x
⋅
a
x
⇒
I
=
l
o
g
(
a
e
)
(
e
a
)
x
+
c