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

The integral from 0 to infinity of xe^{-x/a} is a^2

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

\int_{0}^{\infty} x e^{- \frac{x}{a}} d x

a^{2}

Solution steps

\int_{0}^{\infty} x e^{- \frac{x}{a}} d x

Compute the indefinite integral:

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

Compute the boundaries:

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

= 0 - (- a^{2})

Simplify

= a^{2}

\int_{0}^{N} e^{(- s t)} sin (3 t) d t

\int \frac{1}{7 x + 8} d x

(0.1 x^{2} - 4.2 x + 6.5)^{1.5}

e^{s e c (8 x)}

n = 1 \sum \infty \frac{5}{2 n ^{2} + 1}

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