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Byju's Answer
Standard XII
Mathematics
Factorization Method Form to Remove Indeterminate Form
Evaluate: ∫...
Question
Evaluate:
∫
d
x
x
4
√
1
+
x
2
A
(
2
x
2
+
1
)
√
1
+
x
2
3
x
3
+
c
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B
(
x
2
−
1
)
√
1
−
x
2
3
x
3
+
c
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C
(
2
x
2
−
1
)
√
1
+
x
2
3
x
3
+
c
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D
None of these
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Solution
The correct option is
C
(
2
x
2
−
1
)
√
1
+
x
2
3
x
3
+
c
Given :
∫
d
x
x
4
√
1
+
x
2
=
∫
d
x
x
5
√
1
x
2
+
1
Let :
1
x
2
+
1
=
z
2
⇒
−
2
x
3
d
x
=
2
z
d
z
⇒
d
x
x
3
=
−
z
d
z
∫
d
x
x
3
x
2
√
1
x
2
+
1
=
∫
−
z
(
z
2
−
1
)
d
z
z
=
∫
(
1
−
z
2
)
d
z
=
z
−
z
3
3
=
√
1
x
2
+
1
−
1
3
(
√
1
x
2
+
1
)
2
=
1
3
√
1
x
2
+
1
∣
∣
∣
3
−
(
1
+
1
x
2
)
∣
∣
∣
=
√
x
2
+
1
3
x
(
2
x
2
−
1
x
2
)
=
(
2
x
2
−
1
)
√
x
2
+
1
3
x
3
+
C
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lim
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→
∞
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