What is the integral from 5 to infinity of xe^{-2x} ?

The integral from 5 to infinity of xe^{-2x} is (11)/(4e^{10)}

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integral from 5 to infinity of xe^{-2x}

\int_{5}^{\infty} x e^{- 2 x} d x

\frac{11}{4 e ^{10}}

Decimal

0.00012 \dots

Solution steps

\int_{5}^{\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_{5}^{\infty} x e^{- 2 x} d x = 0 - (- \frac{11}{4 e ^{10}})

= 0 - (- \frac{11}{4 e ^{10}})

Simplify

= \frac{11}{4 e ^{10}}

What is the integral from 5 to infinity of xe^{-2x} ?
The integral from 5 to infinity of xe^{-2x} is (11)/(4e^{10)}