How do you integrate x^2 e^-xx2e−x?

1 Answer
Konstantinos Michailidis
Oct 26, 2015

It is

int x^2*e^-xdx=-e^-x*x^2+int e^-x2xdx=-x^2*e^-x-2x*e^-x+2*int e^-xdx=-e^-x*(x^2+2x+2)+c∫x2⋅e−xdx=−e−x⋅x2+∫e−x2xdx=−x2⋅e−x−2x⋅e−x+2⋅∫e−xdx=−e−x⋅(x2+2x+2)+c

We used integration by parts

int f'(x)*g(x)dx=f(x)*g(x)-intf(x)*g'(x)dx

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