What is the integral from 1 to infinity of xe^{-3x} ?

The integral from 1 to infinity of xe^{-3x} is 4/(9e^3)

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integral from 1 to infinity of xe^{-3x}

\int_{1}^{\infty} x e^{- 3 x} d x

\frac{4}{9 e ^{3}}

Decimal

0.02212 \dots

Solution steps

\int_{1}^{\infty} x e^{- 3 x} d x

Compute the indefinite integral:

\int x e^{- 3 x} d x = \frac{1}{9} (- 3 e^{- 3 x} x - e^{- 3 x}) + C

Compute the boundaries:

\int_{1}^{\infty} x e^{- 3 x} d x = 0 - (- \frac{4}{9 e ^{3}})

= 0 - (- \frac{4}{9 e ^{3}})

Simplify

= \frac{4}{9 e ^{3}}

\frac{d}{d x} (2 x e^{2 x} + e^{2 x} \cdot 2 x^{2})

\frac{d y}{d x} = x (6 - y)

\frac{d}{d x} (\frac{2 x}{1 + 5 x ^{2}})

x y^{^{'}} + 2 y = 4 x

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

What is the integral from 1 to infinity of xe^{-3x} ?
The integral from 1 to infinity of xe^{-3x} is 4/(9e^3)