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Mathematics
Problem
If
l
r
(
x
)
l^{r}(x)
l
r
(
x
)
means
log
log
log
…
x
\log\log\log\dots x
lo
g
lo
g
lo
g
…
x
, the log being repeated
r
r
r
times, then
∫
[
x
l
(
x
)
l
2
(
x
)
l
3
(
x
)
…
l
r
(
x
)
]
−
1
d
x
\int [x\,l(x)\,l^2(x)\,l^3(x)\dots l^r(x)]^{-1}\,dx
∫
[
x
l
(
x
)
l
2
(
x
)
l
3
(
x
)
…
l
r
(
x
)
]
−
1
d
x
is equal to (a)
l
r
+
1
(
x
)
+
C
l^{r+1}(x)+C
l
r
+
1
(
x
)
+
C
(b)
l
r
+
1
(
x
)
r
+
1
+
C
\frac{l^{r+1}(x)}{r+1}+C
r
+
1
l
r
+
1
(
x
)
+
C
(c)
l
r
(
x
)
+
C
l^r(x)+C
l
r
(
x
)
+
C
(d) none of these (a)
l
r
+
1
(
x
)
+
C
l^{r+1}(x)+C
l
r
+
1
(
x
)
+
C
(b)
l
r
+
1
(
x
)
r
+
1
+
C
\frac{l^{r+1}(x)}{r+1}+C
r
+
1
l
r
+
1
(
x
)
+
C
(c)
l
r
(
x
)
+
C
l^r(x)+C
l
r
(
x
)
+
C
(d) none of these
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