What is the integral from 4 to infinity of xe^{-2x} ?

The integral from 4 to infinity of xe^{-2x} is 9/(4e^8)

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integral from 4 to infinity of xe^{-2x}

\int_{4}^{\infty} x e^{- 2 x} d x

\frac{9}{4 e ^{8}}

Decimal Notation

0.00075 \dots

Solution steps

\int_{4}^{\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_{4}^{\infty} x e^{- 2 x} d x = 0 - (- \frac{9}{4 e ^{8}})

= 0 - (- \frac{9}{4 e ^{8}})

Simplify

= \frac{9}{4 e ^{8}}

\int_{- 3}^{5} 2 y - (y^{2} - 15) d y

\frac{\partial}{\partial x} (3 x arctan (\frac{x}{y}))

4 e^{x} + x

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

(x + 1) (4 x^{2} - 4 x - 8)

What is the integral from 4 to infinity of xe^{-2x} ?
The integral from 4 to infinity of xe^{-2x} is 9/(4e^8)