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Mathematics
Mathematics
Problem
If
I
n
=
∫
(
ln
x
)
n
d
x
I_n = \int (\ln x)^n\,dx
I
n
=
∫
(
ln
x
)
n
d
x
, then
I
n
+
n
I
n
−
1
=
I_n + n I_{n-1} =
I
n
+
n
I
n
−
1
=
(a)
(
ln
x
)
n
x
+
C
\frac{(\ln x)^n}{x} + C
x
(
l
n
x
)
n
+
C
(b)
x
(
ln
x
)
n
−
1
+
C
x(\ln x)^{n-1} + C
x
(
ln
x
)
n
−
1
+
C
(c)
x
(
ln
x
)
n
+
C
x(\ln x)^n + C
x
(
ln
x
)
n
+
C
(d) none of these (a)
(
ln
x
)
n
x
+
C
\frac{(\ln x)^n}{x} + C
x
(
l
n
x
)
n
+
C
(b)
x
(
ln
x
)
n
−
1
+
C
x(\ln x)^{n-1} + C
x
(
ln
x
)
n
−
1
+
C
(c)
x
(
ln
x
)
n
+
C
x(\ln x)^n + C
x
(
ln
x
)
n
+
C
(d) none of these
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