∫xe^(-x) dx=?从1积到0
2个回答

∫xe^(-x) dx

=-xe^(-x) -∫(-x)'e^(-x) dx

=-xe^(-x)+∫e^(-x) dx

=-xe^(-x)-e^(-x)

=-(x+1)e^(-x)

从1积到0

[-(0+1)e^0]-[-(1+1)e^(-1)]

=-1+2/e

=(2/e)-1

从2积分到正无穷

[-(正无穷+1)*e^-无穷]-[-(2+1)e^(-2)]

=0+3/e²

=3/e²