What is the integral from 2 to infinity of x/(e^x) ?

The integral from 2 to infinity of x/(e^x) is 3/(e^2)

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integral from 2 to infinity of x/(e^x)

\int_{2}^{\infty} \frac{x}{e ^{x}} d x

\frac{3}{e ^{2}}

Decimal

0.40600 \dots

Solution steps

\int_{2}^{\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_{2}^{\infty} \frac{x}{e ^{x}} d x = 0 - (- \frac{3}{e ^{2}})

= 0 - (- \frac{3}{e ^{2}})

Simplify

= \frac{3}{e ^{2}}

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What is the integral from 2 to infinity of x/(e^x) ?
The integral from 2 to infinity of x/(e^x) is 3/(e^2)