What is the integral from 1 to infinity of x*e^{-2x} ?

The integral from 1 to infinity of x*e^{-2x} is 3/(4e^2)

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integral from 1 to infinity of x*e^{-2x}

\int_{1}^{\infty} x \cdot e^{- 2 x} d x

\frac{3}{4 e ^{2}}

Decimal

0.10150 \dots

Solution steps

\int_{1}^{\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_{1}^{\infty} x e^{- 2 x} d x = 0 - (- \frac{3}{4 e ^{2}})

= 0 - (- \frac{3}{4 e ^{2}})

Simplify

= \frac{3}{4 e ^{2}}

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What is the integral from 1 to infinity of x*e^{-2x} ?
The integral from 1 to infinity of x*e^{-2x} is 3/(4e^2)