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KEAM 2013 Math Paper
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© examsnet.com
Question : 108
Total: 120
∫
(
27
e
9
x
+
e
12
x
)
1
3
d
x
is equal to
(
1
4
)
(
27
+
e
3
x
)
1
3
+
C
(
1
4
)
(
27
+
e
3
x
)
2
3
+
C
(
1
3
)
(
27
+
e
3
x
)
4
3
+
C
(
1
4
)
(
27
+
e
3
x
)
4
3
+
C
(
3
4
)
(
27
+
e
3
x
)
4
3
+
C
Validate
Solution:
Let
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
=
1
3
∫
t
1
/
3
d
t
=
1
3
[
t
4
/
3
]
×
3
4
+
C
⇒
I
=
1
4
(
27
+
e
3
x
)
4
/
3
+
C
© examsnet.com
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