Determine the value of ∫0π/2ln(cos2x+ksin2x)dx\int_{0}^{\pi/2} \ln(\cos^2 x + k \sin^2 x) dx∫0π/2ln(cos2x+ksin2x)dx for k>0k > 0k>0.
πln(1+k2)\pi \ln(\frac{1+\sqrt{k}}{2})πln(21+k)
π2ln(k)\frac{\pi}{2} \ln(k)2πln(k)
πln(1+k)\pi \ln(1+\sqrt{k})πln(1+k)
π2ln(1+k2)\frac{\pi}{2} \ln(\frac{1+k}{2})2πln(21+k)