What is the integral from 0 to infinity of 6xe^{-3x} ?

The integral from 0 to infinity of 6xe^{-3x} is 2/3

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integral from 0 to infinity of 6xe^{-3x}

\int_{0}^{\infty} 6 x e^{- 3 x} d x

\frac{2}{3}

Solution steps

\int_{0}^{\infty} 6 x e^{- 3 x} d x

Compute the indefinite integral:

\int 6 x e^{- 3 x} d x = - 2 e^{- 3 x} x - \frac{2}{3} e^{- 3 x} + C

Compute the boundaries:

\int_{0}^{\infty} 6 x e^{- 3 x} d x = 0 - (- \frac{2}{3})

= 0 - (- \frac{2}{3})

Simplify

= \frac{2}{3}

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What is the integral from 0 to infinity of 6xe^{-3x} ?
The integral from 0 to infinity of 6xe^{-3x} is 2/3