What is the integral of z/(e^{5z)} ?

The integral of z/(e^{5z)} is -1/5 e^{-5z}z-1/25 e^{-5z}+C

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integral of z/(e^{5z)}

\int \frac{z}{e ^{5 z}} d z

- \frac{1}{5} e^{- 5 z} z - \frac{1}{25} e^{- 5 z} + C

Solution steps

\int \frac{z}{e ^{5 z}} d z

Apply Integration By Parts

: - \frac{1}{5} e^{- 5 z} z - \int - \frac{1}{5} e^{- 5 z} d z

= - \frac{1}{5} e^{- 5 z} z - \int - \frac{1}{5} e^{- 5 z} d z

\int - \frac{1}{5} e^{- 5 z} d z = \frac{1}{25} e^{- 5 z}

= - \frac{1}{5} e^{- 5 z} z - \frac{1}{25} e^{- 5 z}

Add a constant to the solution

= - \frac{1}{5} e^{- 5 z} z - \frac{1}{25} e^{- 5 z} + C

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What is the integral of z/(e^{5z)} ?
The integral of z/(e^{5z)} is -1/5 e^{-5z}z-1/25 e^{-5z}+C