Is there a way to solve integral containing square of incomplete gamma function?

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Is there a way to solve such an integral: $$\int\frac{\Gamma(a,x)^2}{x^2}dx$$ in terms of known functions? The free online version of the WolframAlpha tool does not provide any solution for it. For the function without square of the incomplete gamma function $$\int\frac{\Gamma(a,x)}{x^2}dx$$ the tool gives solution in terms of incomplete gamma function itself $$\Gamma(a-1,x)-\frac{\Gamma(a,x)}{x}$$Could a similar solution exist for the first equation above where the square of the incomplete gamma function is used under integral?