Calculate ${\int}_{0}^{1}\frac{{\mathrm{log}}^{2}x\mathrm{log}(1+{x}^{2})}{1-{x}^{2}}dx$

I found $-{\displaystyle \frac{{\pi}^{4}}{32}}+2{G}^{2}+{\displaystyle \frac{7}{4}}\zeta (3)\mathrm{log}2$ where $G$ is the Catalan's constant.

I found $-{\displaystyle \frac{{\pi}^{4}}{32}}+2{G}^{2}+{\displaystyle \frac{7}{4}}\zeta (3)\mathrm{log}2$ where $G$ is the Catalan's constant.