广义积分∫ (正无穷,0) x/(1+x)^3 dx
=∫ (正无穷,1)(x-1)/x^{3}dx
=∫ (正无穷,1)(x^{-2}-x^{-3})dx
=(-x^{-1}+1/2x^{-2}) | (正无穷,1)
=1/2