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IMC 1995 Problem 4
IMC 1995 Problem 4
Source: IMC 1995
February 18, 2021
real analysis
Problem Statement
Let
F
:
(
1
,
∞
)
→
R
F:(1,\infty) \rightarrow \mathbb{R}
F
:
(
1
,
∞
)
→
R
be the function defined by
F
(
x
)
=
∫
x
x
2
d
t
ln
(
t
)
.
F(x)=\int_{x}^{x^{2}} \frac{dt}{\ln(t)}.
F
(
x
)
=
∫
x
x
2
ln
(
t
)
d
t
.
Show that
F
F
F
is injective and find the set of values of
F
F
F
.
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