I'm a bit stumped with a problem I have recently seen. Here it is:(adsbygoogle = window.adsbygoogle || []).push({});

There is a continuous and decreasing function [tex]y(x):[0,1] \to [0,1],\mbox{ }0<a<b[/tex] and [tex]x^a-x^b=y^a-y^b[/tex]

Prove that [tex]\int_{0}^{1} \frac{\ln y}{x} dx=-\frac{\pi ^2}{3ab}[/tex]

The trivial solution of y=x causes the integral to diverge. Frankly, I'm at a loss on how to approach this problem. Clearly you cannot solve for y in general as a and b can also take on non-integer values.

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# Integral from Unsolvable Equation

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