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Traian Lălescu
2005 Traian Lălescu
2005 Traian Lălescu
Part of
Traian Lălescu
Subcontests
(1)
1
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Bijectivity of integral function
4.
\fbox{4.}
4.
Prove that the function
F
:
(
1
;
∞
)
→
(
ln
2
;
∞
)
F:(1;\infty)\to(\ln 2;\infty)
F
:
(
1
;
∞
)
→
(
ln
2
;
∞
)
defined by
F
(
x
)
=
∫
x
x
2
1
ln
t
d
t
F(x)=\int\limits_x^{x^2} \frac{1}{\ln t}\ \mathrm{d}t
F
(
x
)
=
x
∫
x
2
ln
t
1
d
t
is bijective.