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

The integral from 0 to infinity of kxe^{-2x} is k/4

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

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

\frac{k}{4}

Solution steps

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

Compute the indefinite integral:

\int k x e^{- 2 x} d x = \frac{1}{4} k (- 2 e^{- 2 x} x - e^{- 2 x}) + C

Compute the boundaries:

\int_{0}^{\infty} k x e^{- 2 x} d x = 0 - (- \frac{1}{4} k)

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

Simplify

= \frac{k}{4}

What is the integral from 0 to infinity of kxe^{-2x} ?
The integral from 0 to infinity of kxe^{-2x} is k/4