What is the integral from 1 to 5 of x/(e^x) ?

The integral from 1 to 5 of x/(e^x) is -6/(e^5)+2/e

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integral from 1 to 5 of x/(e^x)

\int_{1}^{5} \frac{x}{e ^{x}} d x

- \frac{6}{e ^{5}} + \frac{2}{e}

Decimal Notation

0.69533 \dots

Solution steps

\int_{1}^{5} \frac{x}{e ^{x}} d x

Apply Integration By Parts

: [- \frac{x}{e ^{x}} - \int - \frac{1}{e ^{x}} d x]_{1}^{5}

= [- \frac{x}{e ^{x}} - \int - \frac{1}{e ^{x}} d x]_{1}^{5}

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

= [- \frac{x}{e ^{x}} - \frac{1}{e ^{x}}]_{1}^{5}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= [\frac{- x - 1}{e ^{x}}]_{1}^{5}

Compute the boundaries:

- \frac{6}{e ^{5}} + \frac{2}{e}

= - \frac{6}{e ^{5}} + \frac{2}{e}

x^{2} - 6 x

f (x) = \frac{3}{x - 2}

- 4 cos (3 t)

\int \frac{10800 q}{9 q ^{2} + 675} d q

\int \frac{( arctan ( x ) )}{1 + x ^{2}} d x

What is the integral from 1 to 5 of x/(e^x) ?
The integral from 1 to 5 of x/(e^x) is -6/(e^5)+2/e