Evaluate the integral I=∫0π/2ln(sin2x+cos2x⋅ea)dxI = \int_0^{\pi/2} \ln(\sin^2 x + \cos^2 x \cdot e^a) dxI=∫0π/2ln(sin2x+cos2x⋅ea)dx where aaa is a constant.
π2ln(1+ea2)\frac{\pi}{2} \ln(\frac{1+e^a}{2})2πln(21+ea)
π2ln(1+ea/22)\frac{\pi}{2} \ln(\frac{1+e^{a/2}}{2})2πln(21+ea/2)
π4ln(ea)\frac{\pi}{4} \ln(e^a)4πln(ea)
π2ln(1+ea)\frac{\pi}{2} \ln(1+e^a)2πln(1+ea)