What is the integral from-infinity to 0 of x5^{-x^2} ?

The integral from-infinity to 0 of x5^{-x^2} is -1/(2ln(5))

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integral from-infinity to 0 of x5^{-x^2}

\int_{- \infty}^{0} x 5^{- x^{2}} d x

- \frac{1}{2 ln ( 5 )}

Decimal

- 0.31066 \dots

Solution steps

\int_{- \infty}^{0} x \cdot 5^{- x^{2}} d x

Compute the indefinite integral:

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

Compute the boundaries:

\int_{- \infty}^{0} x \cdot 5^{- x^{2}} d x = - \frac{1}{2 ln ( 5 )} - 0

= - \frac{1}{2 ln ( 5 )} - 0

Simplify

= - \frac{1}{2 ln ( 5 )}

What is the integral from-infinity to 0 of x5^{-x^2} ?
The integral from-infinity to 0 of x5^{-x^2} is -1/(2ln(5))