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Byju's Answer
Standard XIII
Mathematics
Integration by Substitution
The value of ...
Question
The value of
∫
d
x
x
n
(
1
+
x
n
)
1
n
,
n
ϵ
N
A
1
1
−
n
{
1
+
1
x
n
}
1
−
1
n
+
c
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B
1
1
+
n
{
1
−
1
x
n
}
1
−
1
n
+
c
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C
−
1
1
−
n
{
1
−
1
x
n
}
1
−
1
n
+
c
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D
1
1
−
n
{
1
+
1
x
n
}
1
−
1
n
+
c
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Solution
The correct option is
D
1
1
−
n
{
1
+
1
x
n
}
1
−
1
n
+
c
I
=
∫
d
x
x
n
(
1
+
x
n
)
1
/
n
=
∫
d
x
x
n
+
1
(
1
+
1
x
n
)
1
/
n
L
e
t
1
+
1
x
n
=
t
⇒
−
n
x
n
+
1
d
x
=
d
t
∴
I
=
−
1
n
∫
d
t
t
1
n
=
−
1
n
⎡
⎣
t
−
1
n
+
1
−
1
n
+
1
⎤
⎦
+
c
=
−
(
1
+
1
x
n
)
1
−
1
n
n
−
1
+
c
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5
Similar questions
Q.
The value of
∫
d
x
x
n
(
1
+
x
n
)
1
n
,
n
ϵ
N
Q.
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∫
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n
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n
)
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/
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The value of
∫
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x
x
n
(
1
+
x
n
)
1
n
,
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ϵ
N
Q.
∫
d
x
x
n
+
1
(
1
+
x
n
)
1
/
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Q.
If
f
(
x
)
=
(
a
−
x
n
)
1
n
,
a
>
0
and
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ϵ
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, then prove that
f
(
f
(
x
)
)
=
x
for all
x
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