Determine the value of the integral I=∫01ln(x)ln(1+x)x dxI = \int_0^1 \frac{\ln(x) \ln(1+x)}{x} \, dxI=∫01xln(x)ln(1+x)dx.
−π324-\frac{\pi^3}{24}−24π3
−π212-\frac{\pi^2}{12}−12π2
π312\frac{\pi^3}{12}12π3
π26\frac{\pi^2}{6}6π2