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Putnam
1993 Putnam
A5
Putnam 1993 A5
Putnam 1993 A5
Source: 1993 Putnam
October 26, 2020
Putnam
real analysis
Problem Statement
Let U be the set formed as the union of three open intervals,
U
=
(
−
100
,
−
10
)
∪
(
1
/
101
,
1
/
11
)
∪
(
101
/
100
,
11
/
10
)
U = (-100, -10) \cup (1/101, 1/11) \cup (101/100, 11/10)
U
=
(
−
100
,
−
10
)
∪
(
1/101
,
1/11
)
∪
(
101/100
,
11/10
)
. Show that
∫
U
(
x
2
−
x
)
2
(
x
3
−
3
x
+
1
)
2
d
x
\int_{U} \frac{(x^2-x)^2}{(x^3-3x+1)^2} dx
∫
U
(
x
3
−
3
x
+
1
)
2
(
x
2
−
x
)
2
d
x
is rational.
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