What is the integral from-infinity to 0 of x5^{-x} ?

The integral from-infinity to 0 of x5^{-x} is diverges

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integral from-infinity to 0 of x5^{-x}

\int_{- \infty}^{0} x 5^{- x} d x

diverges

Solution steps

\int_{- \infty}^{0} x \cdot 5^{- x} d x

Compute the indefinite integral:

\int x \cdot 5^{- x} d x = - \frac{5 ^{- x} x}{ln ( 5 )} - \frac{1}{ln ^{2} ( 5 )} \cdot 5^{- x} + C

Compute the boundaries:

\int_{- \infty}^{0} x \cdot 5^{- x} d x =

diverges

= diverges

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What is the integral from-infinity to 0 of x5^{-x} ?
The integral from-infinity to 0 of x5^{-x} is diverges