What is the integral from 0 to infinity of 2e^{-2x}x ?

The integral from 0 to infinity of 2e^{-2x}x is 1/2

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integral from 0 to infinity of 2e^{-2x}x

\int_{0}^{\infty} 2 e^{- 2 x} x d x

\frac{1}{2}

Decimal

0.5

Solution steps

\int_{0}^{\infty} 2 e^{- 2 x} x d x

Compute the indefinite integral:

\int 2 e^{- 2 x} x d x = - e^{- 2 x} x - \frac{1}{2} e^{- 2 x} + C

Compute the boundaries:

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

= 0 - (- \frac{1}{2})

Simplify

= \frac{1}{2}

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What is the integral from 0 to infinity of 2e^{-2x}x ?
The integral from 0 to infinity of 2e^{-2x}x is 1/2