What is the integral from 0 to infinity of 4xe^{-4x} ?

The integral from 0 to infinity of 4xe^{-4x} is 1/4

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integral from 0 to infinity of 4xe^{-4x}

\int_{0}^{\infty} 4 x e^{- 4 x} d x

\frac{1}{4}

Decimal

0.25

Solution steps

\int_{0}^{\infty} 4 x e^{- 4 x} d x

Compute the indefinite integral:

\int 4 x e^{- 4 x} d x = - e^{- 4 x} x - \frac{1}{4} e^{- 4 x} + C

Compute the boundaries:

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

= 0 - (- \frac{1}{4})

Simplify

= \frac{1}{4}

What is the integral from 0 to infinity of 4xe^{-4x} ?
The integral from 0 to infinity of 4xe^{-4x} is 1/4