What is the integral from infinity to 0 of xe^x ?

The integral from infinity to 0 of xe^x is diverges

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integral from infinity to 0 of xe^x

\int_{\infty}^{0} x e^{x} d x

diverges

Solution steps

\int_{\infty}^{0} x e^{x} d x

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{0}^{\infty} x e^{x} d x

\int_{0}^{\infty} x e^{x} d x =

diverges

= diverges

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What is the integral from infinity to 0 of xe^x ?
The integral from infinity to 0 of xe^x is diverges