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

The integral from c to infinity of xe^{-2x} is -1/4 (-2ce^{-2c}-e^{-2c})

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

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

- \frac{1}{4} (- 2 c e^{- 2 c} - e^{- 2 c})

Solution steps

\int_{c}^{\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_{c}^{\infty} x e^{- 2 x} d x = 0 - \frac{1}{4} (- 2 e^{- 2 c} c - e^{- 2 c})

= 0 - \frac{1}{4} (- 2 e^{- 2 c} c - e^{- 2 c})

Simplify

= - \frac{1}{4} (- 2 c e^{- 2 c} - e^{- 2 c})

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What is the integral from c to infinity of xe^{-2x} ?
The integral from c to infinity of xe^{-2x} is -1/4 (-2ce^{-2c}-e^{-2c})