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

The integral from 6 to infinity of xe^{-2x} is (13)/(4e^{12)}

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integral from 6 to infinity of xe^{-2x}

\int_{6}^{\infty} x e^{- 2 x} d x

\frac{13}{4 e ^{12}}

Decimal

0.00001 \dots

Solution steps

\int_{6}^{\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_{6}^{\infty} x e^{- 2 x} d x = 0 - (- \frac{13}{4 e ^{12}})

= 0 - (- \frac{13}{4 e ^{12}})

Simplify

= \frac{13}{4 e ^{12}}

What is the integral from 6 to infinity of xe^{-2x} ?
The integral from 6 to infinity of xe^{-2x} is (13)/(4e^{12)}