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

The integral from 2 to infinity of xe^{-2x} is 5/(4e^4)

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

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

\frac{5}{4 e ^{4}}

Decimal Notation

0.02289 \dots

Solution steps

\int_{2}^{\infty} 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_{2}^{\infty} x e^{- 2 x} d x = 0 - (- \frac{5}{4 e ^{4}})

= 0 - (- \frac{5}{4 e ^{4}})

Simplify

= \frac{5}{4 e ^{4}}

\frac{\partial}{\partial x} (y x - y - x)

\frac{d}{d x} (\frac{( 1 + tan ( x ) ) ^{2}}{sec ( x )})

(ln (\frac{x}{2}))^{^{'}}

y^{^{'}} = 5 x - y

\int 15 + \frac{200}{x + 1} d x

What is the integral from 2 to infinity of xe^{-2x} ?
The integral from 2 to infinity of xe^{-2x} is 5/(4e^4)