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Question
Mathematics
If In= displaystyle ∫ (ln x)ndx , then I10+10I9 is equal to (where C is the constant of integration)
Q. If
I
n
=
∫
(
l
n
x
)
n
d
x
, then
I
10
+
10
I
9
is equal to (where
C
is the constant of integration)
1597
186
NTA Abhyas
NTA Abhyas 2020
Integrals
Report Error
A
x
(
l
n
x
)
10
+
C
0%
B
10
(
l
n
x
)
9
+
C
100%
C
9
(
l
n
x
)
10
+
C
0%
D
x
(
l
n
x
)
9
+
C
0%
Solution:
I
n
=
∫
(
l
n
x
)
n
d
x
I
n
=
x
(
l
n
x
)
n
−
∫
x
x
n
(
l
n
x
)
n
−
1
d
x
I
n
=
x
(
l
n
x
)
n
−
(
n
I
)
n
−
1
I
n
+
n
I
n
−
1
=
x
(
l
n
x
)
n
+
C
I
10
+
10
I
9
=
x
(
l
n
x
)
10
+
C