Evaluate the integral I=∫0π/4ln(1+tanx)cos2xdxI = \int_{0}^{\pi/4} \frac{\ln(1+\tan x)}{\cos^2 x} dxI=∫0π/4cos2xln(1+tanx)dx.
12ln2\frac{1}{2} \ln 221ln2
14ln2\frac{1}{4} \ln 241ln2
π8ln2\frac{\pi}{8} \ln 28πln2
ln2\ln 2ln2