What is the integral of z/(e^{8z)} ?

The integral of z/(e^{8z)} is -1/8 e^{-8z}z-1/64 e^{-8z}+C

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integral of z/(e^{8z)}

\int \frac{z}{e ^{8 z}} d z

- \frac{1}{8} e^{- 8 z} z - \frac{1}{64} e^{- 8 z} + C

Solution steps

\int \frac{z}{e ^{8 z}} d z

Apply Integration By Parts

= - \frac{1}{8} e^{- 8 z} z - \int - \frac{1}{8} e^{- 8 z} d z

\int - \frac{1}{8} e^{- 8 z} d z = \frac{1}{64} e^{- 8 z}

= - \frac{1}{8} e^{- 8 z} z - \frac{1}{64} e^{- 8 z}

Add a constant to the solution

= - \frac{1}{8} e^{- 8 z} z - \frac{1}{64} e^{- 8 z} + C

What is the integral of z/(e^{8z)} ?
The integral of z/(e^{8z)} is -1/8 e^{-8z}z-1/64 e^{-8z}+C