Determine the value of I=∫0π/2ln(sinx)sin2x+cos2xdxI = \int_{0}^{\pi/2} \frac{\ln(\sin x)}{\sin^2 x + \cos^2 x} dxI=∫0π/2sin2x+cos2xln(sinx)dx.
−π2ln2-\frac{\pi}{2} \ln 2−2πln2
−πln2-\pi \ln 2−πln2
000
ln(π/2)\ln(\pi/2)ln(π/2)