What is the integral of y/(e^y) ?

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

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integral of y/(e^y)

\int \frac{y}{e ^{y}} d y

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

Solution steps

\int \frac{y}{e ^{y}} d y

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

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