What is the integral from 2 to infinity of 4xe^{-2x} ?

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

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integral from 2 to infinity of 4xe^{-2x}

\int_{2}^{\infty} 4 x e^{- 2 x} d x

\frac{5}{e ^{4}}

Decimal Notation

0.09157 \dots

Solution steps

\int_{2}^{\infty} 4 x e^{- 2 x} d x

Compute the indefinite integral:

\int 4 x e^{- 2 x} d x = - 2 e^{- 2 x} x - e^{- 2 x} + C

Compute the boundaries:

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

= 0 - (- \frac{5}{e ^{4}})

Simplify

= \frac{5}{e ^{4}}

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