判别下列各反常积分的收敛性,如果收敛,计算反常积分的值.

Sln(x)dx = xln(x) - Sdx = xln(x) - x + C,

lim_{x->0+}[xln(x) - x] = lim_{x->0+}xln(x) = lim_{x->0+}ln(x)/(1/x) = lim_{x->0+}(1/x)/(-1/x^2) = lim_{x->0+}(-x) = 0.

(1)收敛.原式=[xln(x) - x]|_{x:0->1} = -1 - 0 = -1.

Sdx/(x^2 - 4x + 3) = Sdx/[(x-1)(x-3)] = (1/2)Sdx/(x-3) - (1/2)Sdx/(x-1)
= (1/2)ln|x-3| - (1/2)ln|x-1| + C,

lim_{x->1}[(1/2)ln|x-3| - (1/2)ln|x-1|} = 无穷大,发散.
（2）发散.