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KEAM 2014 Math Paper
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© examsnet.com
Question : 39
Total: 120
∫
1
x
2
(
x
4
+
1
)
3
4
dx
is equal to
−
(
1
+
x
4
)
3
4
x
+
C
−
(
1
+
x
4
)
1
4
2
x
+
C
−
(
1
+
x
4
)
1
4
x
+
C
−
(
1
+
x
4
)
1
4
x
2
+
C
−
(
1
+
x
4
)
1
2
x
+
C
Validate
Solution:
Let
I
=
∫
1
x
2
(
x
4
+
1
)
3
/
4
d
x
=
∫
1
x
2
⋅
x
3
(
1
+
1
x
4
)
3
/
4
d
x
=
∫
1
x
5
(
1
+
1
x
4
)
−
3
∕
4
d
x
Put
1
+
1
x
4
=
t
⇒
−
4
x
5
d
x
=
d
t
∴
I
=
−
1
4
∫
t
−
3
/
4
d
t
=
−
1
4
⋅
t
1
/
4
1
/
4
+
C
=
−
(
1
+
1
x
4
)
1
/
4
+
C
=
−
(
x
4
+
1
x
4
)
1
/
4
+
C
=
−
(
x
4
+
1
)
1
∕
4
x
+
C
© examsnet.com
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