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

The integral from 0 to infinity of x*e^{-4x} is 1/16

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

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

\frac{1}{16}

Decimal

0.0625

Solution steps

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

Compute the indefinite integral:

\int x e^{- 4 x} d x = \frac{1}{16} (- 4 e^{- 4 x} x - e^{- 4 x}) + C

Compute the boundaries:

\int_{0}^{\infty} x e^{- 4 x} d x = 0 - (- \frac{1}{16})

= 0 - (- \frac{1}{16})

Simplify

= \frac{1}{16}

What is the integral from 0 to infinity of x*e^{-4x} ?
The integral from 0 to infinity of x*e^{-4x} is 1/16