What is the integral from 0 to infinity of x/(e^x) ?

The integral from 0 to infinity of x/(e^x) is 1

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integral from 0 to infinity of x/(e^x)

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

1

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

= 0 - (- 1)

Simplify

= 1

\int_{1}^{e} ln (4 x) d x

(1 - x^{2}) \frac{d y}{d x} = x e^{y}

x \to + 5 lim (\frac{( x + 1 )}{x - 5})

x = 2 3 y, x = 0, y = 9

x \to - 2 lim ((x - 1)^{3})

What is the integral from 0 to infinity of x/(e^x) ?
The integral from 0 to infinity of x/(e^x) is 1