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

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

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integral of z/(e^z)

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

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