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

The integral of x 1/(e^x) is -x/(e^x)-1/(e^x)+C

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integral of x 1/(e^x)

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

- \frac{x}{e ^{x}} - \frac{1}{e ^{x}} + C

Solution steps

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

Simplify

x \frac{1}{e ^{x}} : \frac{x}{e ^{x}}

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

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What is the integral of x 1/(e^x) ?
The integral of x 1/(e^x) is -x/(e^x)-1/(e^x)+C