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Bijectivity of integral function

Source: "Traian Lalescu" Contest , Arad, 2005,XIIth grade, Problem 4

March 14, 2014
calculusintegrationfunctionlogarithmsalgebradomainlimit

Problem Statement

4.\fbox{4.} Prove that the function F:(1;∞)→(ln⁡2;∞)F:(1;\infty)\to(\ln 2;\infty) defined by F(x)=∫xx21ln⁡t dt F(x)=\int\limits_x^{x^2} \frac{1}{\ln t}\ \mathrm{d}t is bijective.
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