Evaluate the integral I=∫01ln(x)1−xdxI = \int_0^1 \frac{\ln(x)}{\sqrt{1-x}} dxI=∫011−xln(x)dx by utilizing the Beta function B(a,b)=∫01xa−1(1−x)b−1dxB(a, b) = \int_0^1 x^{a-1}(1-x)^{b-1} dxB(a,b)=∫01xa−1(1−x)b−1dx.
−4ln(2)-4 \ln(2)−4ln(2)
−2ln(2)-2 \ln(2)−2ln(2)
4ln(2)4 \ln(2)4ln(2)
2ln(2)2 \ln(2)2ln(2)