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How do you integrate #x^2 e^-x#?

Answer 1

Ezekiel Alexander

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#

Integration by portions was employed.

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

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Answer 2

Paisley Johnson

To integrate ( x^2 e^{-x} ), you can use integration by parts. Let ( u = x^2 ) and ( dv = e^{-x} dx ), then differentiate ( u ) and integrate ( dv ) to find ( du ) and ( v ). After that, apply the integration by parts formula: [ \int u , dv = uv - \int v , du ]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.