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Question
Mathematics
∫(27e9x+e12x)1/3dx is equal to
Q.
∫
(
27
e
9
x
+
e
12
x
)
1/3
d
x
is equal to
1581
212
KEAM
KEAM 2013
Integrals
Report Error
A
(
1/4
)
(
27
+
e
3
x
)
1/3
+
C
B
(
1/4
)
(
27
+
e
3
x
)
2/3
+
C
C
(
1/3
)
(
27
+
e
3
x
)
4/3
+
C
D
(
1/4
)
(
27
+
e
3
x
)
4/3
+
C
E
(
3/4
)
(
27
+
e
3
x
)
4/3
+
C
Solution:
I
=
∫
(
27
e
9
x
+
e
12
x
)
1/3
d
x
=
∫
(
e
9
x
)
1/3
{
27
+
e
3
x
}
1/3
d
x
=
∫
e
3
x
(
27
+
e
3
x
)
1/3
d
x
Put
t
=
27
+
e
3
x
⇒
d
t
=
3
e
3
x
d
x
⇒
I
=
3
1
∫
t
1/3
d
t
=
3
1
[
t
4/3
]
×
4
3
+
C
⇒
I
=
4
1
(
27
+
e
3
x
)
4/3
+
C