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KEAM 2015 Math Paper
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© examsnet.com
Question : 11
Total: 120
∫
(
x
+
1
)
2
x
(
x
2
+
1
)
d
x
=
log
|
x
(
x
2
+
1
)
|
+
C
log
|
x
|
+
C
log
|
x
|
+
2
t
a
n
−
1
x
+
C
log
(
1
1
+
x
2
)
+
C
2
log
|
x
|
+
t
a
n
−
1
x
+
C
Validate
Solution:
Let
I
=
∫
(
x
+
1
)
2
x
(
x
2
+
1
)
d
x
=
∫
x
2
+
1
+
2
x
x
(
x
2
+
1
)
d
x
=
∫
x
2
+
1
x
(
x
2
+
1
)
d
x
+
∫
2
x
x
(
x
2
+
1
)
d
x
=
∫
1
x
d
x
+
2
∫
1
x
2
+
1
d
x
=
log
|
x
|
+
2
tan
−
1
x
+
C
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