What is the integral from 4 to infinity of xe^{-5x} ?

The integral from 4 to infinity of xe^{-5x} is (21)/(25e^{20)}

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integral from 4 to infinity of xe^{-5x}

\int_{4}^{\infty} x e^{- 5 x} d x

\frac{21}{25 e ^{20}}

Decimal

1.73137 E - 9

Solution steps

\int_{4}^{\infty} x e^{- 5 x} d x

Compute the indefinite integral:

\int x e^{- 5 x} d x = \frac{1}{25} (- 5 e^{- 5 x} x - e^{- 5 x}) + C

Compute the boundaries:

\int_{4}^{\infty} x e^{- 5 x} d x = 0 - (- \frac{21}{25 e ^{20}})

= 0 - (- \frac{21}{25 e ^{20}})

Simplify

= \frac{21}{25 e ^{20}}

(y^{2} + x y^{2}) \frac{d y}{d x} = 1

x \to - 1 lim (\frac{4 x ^{2} + 1}{x})

\int - x \cdot e^{- x} d x

\int \frac{e ^{2 x} + 2 e ^{x}}{e ^{2 x} - 8} d x

y^{^{'}} - y = 5 x - 5, y (0) = 9

What is the integral from 4 to infinity of xe^{-5x} ?
The integral from 4 to infinity of xe^{-5x} is (21)/(25e^{20)}