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 Notation

- 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 )}

\int 16 + y^{2} d y

\frac{\partial}{\partial x} (54 x^{8} y^{5} - 40 x^{7} y^{4})

\int \frac{ln ( x )}{x} d x

f (x) = (3) e - 5 x

\frac{d}{d x} ((x^{2} + 4)^{2})

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))