Given that $$\int_{1/\phi}^{1/\phi^2}{ \dfrac{\ln(1-x)}{x}}dx=\dfrac{\pi^2}{30}$$ Find the value of $$\int_{1/\phi}^{1/\phi^2} \left(\dfrac{\ln(1-x)}{x}\right)^2 dx$$ in terms of $\phi$ and $\pi$. Where $\phi=\frac{1+\sqrt 5}{2}$ is the golden ratio.
I have tried to do it by taylor series, also tried integration by parts but it is getting ugly and too many terms are coming.
Source: Made by Prof. Raghava.
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