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Question Number 129319 by snipers237 last updated on 14/Jan/21

$$Provethat$$$$iffissuchasf{}^{\prime }\left(x\right)=\frac{f\left(x\right)}{x(1-x-f\left(x\right))}$$$$andf\left(1\right)=0butf\ncong \mathrm{\Theta }.Then$$$$★fistheuniquebijectionfrom{\mathbb{R}}^{\ast }to\mathbb{R}and$$$$★\underset{x\to 0}{\lim }f\left(x\right)=+\mathrm{\infty }and\underset{x\to 0}{\lim }xf\left(x\right)=0$$$$★{\int }_0^{+\mathrm{\infty }}{f}^{-1}\left(y\right)dy=\zeta \left(2\right)={\int }_0^{1}f\left(x\right)dx$$$$$$$$$$$$$$$$$$

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