What is the integral from-infinity to 0 of xe^{-2x} ?

The integral from-infinity to 0 of xe^{-2x} is diverges

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integral from-infinity to 0 of xe^{-2x}

\int_{- \infty}^{0} x e^{- 2 x} d x

diverges

Solution steps

\int_{- \infty}^{0} x e^{- 2 x} d x

Compute the indefinite integral:

\int x e^{- 2 x} d x = \frac{1}{4} (- 2 e^{- 2 x} x - e^{- 2 x}) + C

Compute the boundaries:

\int_{- \infty}^{0} x e^{- 2 x} d x =

diverges

= diverges

What is the integral from-infinity to 0 of xe^{-2x} ?
The integral from-infinity to 0 of xe^{-2x} is diverges