Evaluate ${\int}_{0}^{1}{\mathrm{log}}^{2}(1-x){\mathrm{log}}^{2}(x)\phantom{\rule{thinmathspace}{0ex}}dx$

I have no idea where to even start. WolframAlpha cant compute it either.

${\int}_{0}^{1}{\mathrm{log}}^{2}(1-x){\mathrm{log}}^{2}(x)\phantom{\rule{thinmathspace}{0ex}}dx$

I think it can be done with series, but I am not sure, can someone help a little so I can get a start??

Thanks!

I have no idea where to even start. WolframAlpha cant compute it either.

${\int}_{0}^{1}{\mathrm{log}}^{2}(1-x){\mathrm{log}}^{2}(x)\phantom{\rule{thinmathspace}{0ex}}dx$

I think it can be done with series, but I am not sure, can someone help a little so I can get a start??

Thanks!