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2013 CIIM
Problem 2
CIIM 2013 Problem 2
CIIM 2013 Problem 2
Source:
August 8, 2016
CIIM 2013
CIIM
undergraduate
Problem Statement
Consider a polinomial
p
∈
R
[
x
]
p \in \mathbb{R}[x]
p
∈
R
[
x
]
of degree
n
n
n
and with no real roots. Prove that
∫
−
∞
∞
(
p
′
(
x
)
)
2
(
p
(
x
)
)
2
+
(
p
′
(
x
)
)
2
d
x
\int_{-\infty}^{\infty}\frac{(p'(x))^2}{(p(x))^2+(p'(x))^2}dx
∫
−
∞
∞
(
p
(
x
)
)
2
+
(
p
′
(
x
)
)
2
(
p
′
(
x
)
)
2
d
x
converges, and is less or equal than
n
3
/
2
π
.
n^{3/2}\pi.
n
3/2
π
.
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