∫ 1/√(x-x²)dx
=∫ 1/√(1/4-1/4+x-x²)dx
=∫ 1/√(1/4-(x-1/2)²)dx
=∫ 1/√(1/4-(x-1/2)²)d(x-1/2)
=arcsin(x-1/2)/(1/2)+c
=arcsin(2x-1)+c