∫(0→∞)xe^(-x²)dx
=½∫(0→∞)e^(-x²)dx²
=e^(-x²)(0→∞)
=-½(0-1)
= ½
∫(0→1)lnx dx
=xlnx(0→1) - ∫(0→1)x(1/x)dx[分部积分]
=1ln1 - xlnx (x→0) -∫(0→1)dx
= 0 - xlnx (x→0) -x(0→1)
=-xlnx(x→0) - 1
= - (lnx)/(1/x)(x→0) - 1
= -(1/x)/(-1/x²)(x→0) - 1[运用了罗毕达方法]
= x(x→0) - 1
= 0 - 1
= -1