∫xe^(x^2)dx=(1/2)∫e^(x^2)d(x^2)=(1/2)e^(x^2)+C(C为常数)代入上下限,可知原积分=(e-1)/2
∫(0→1) xe^x² dx= ∫(0→1) e^x² d(x²/2)= (1/2)[e^x²] |(0,1)= (1/2)(e^1 - e^0)= (e - 1)/2