Determine the value of the integral I=∫1e2ln(x)x(1+ln2(x))dxI = \int_{1}^{e^2} \frac{\ln(x)}{x(1 + \ln^2(x))} dxI=∫1e2x(1+ln2(x))ln(x)dx.
12ln(5)\frac{1}{2} \ln(5)21ln(5)
12ln(2)\frac{1}{2} \ln(2)21ln(2)
ln(2)\ln(2)ln(2)
π/4\pi/4π/4