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

The integral from 2 to infinity of xe^{-x^2} is 1/(2e^4)

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

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

\frac{1}{2 e ^{4}}

Decimal

0.00915 \dots

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

\int_{2}^{\infty} x e^{- x^{2}} d x = 0 - (- \frac{1}{2 e ^{4}})

= 0 - (- \frac{1}{2 e ^{4}})

Simplify

= \frac{1}{2 e ^{4}}

\frac{d}{d x} (4 - x)

\int \frac{sinh ( x )}{1 + cosh ( x )} d x

\frac{d y}{d x} = \frac{2 y}{x ^{2} - 1}

x sin^{2} (x)

3 x^{2} e^{x} + e^{x} x^{3}

What is the integral from 2 to infinity of xe^{-x^2} ?
The integral from 2 to infinity of xe^{-x^2} is 1/(2e^4)