Evaluate the definite integral I=∫0π/2sin2xsinx+cosxdxI = \int_{0}^{\pi/2} \frac{\sin^2 x}{\sin x + \cos x} dxI=∫0π/2sinx+cosxsin2xdx given that ∫0π/2cos2xsinx+cosxdx=12ln(1+2)\int_{0}^{\pi/2} \frac{\cos^2 x}{\sin x + \cos x} dx = \frac{1}{\sqrt{2}} \ln(1+\sqrt{2})∫0π/2sinx+cosxcos2xdx=21ln(1+2).
12ln(1+2)\frac{1}{\sqrt{2}} \ln(1+\sqrt{2})21ln(1+2)
12ln(2−1)\frac{1}{\sqrt{2}} \ln(\sqrt{2}-1)21ln(2−1)
1−12ln(1+2)1 - \frac{1}{\sqrt{2}} \ln(1+\sqrt{2})1−21ln(1+2)
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