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

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

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

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

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

Decimal

0.09157 \dots

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

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

Simplify

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

f (r) = r + 7 r

\int (2 x e^{- 3 x}) d x

x \to 0 lim (\frac{3 tan ( x )}{x})

y^{^{'}} + 2 sin (2 x) y = 2 sin (2 x), y (\frac{π}{2}) = 3

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

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