What is the integral of z/(e^{6z)} ?

The integral of z/(e^{6z)} is -1/6 e^{-6z}z-1/36 e^{-6z}+C

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integral of z/(e^{6z)}

\int \frac{z}{e ^{6 z}} d z

- \frac{1}{6} e^{- 6 z} z - \frac{1}{36} e^{- 6 z} + C

Solution steps

\int \frac{z}{e ^{6 z}} d z

Apply Integration By Parts

: - \frac{1}{6} e^{- 6 z} z - \int - \frac{1}{6} e^{- 6 z} d z

= - \frac{1}{6} e^{- 6 z} z - \int - \frac{1}{6} e^{- 6 z} d z

\int - \frac{1}{6} e^{- 6 z} d z = \frac{1}{36} e^{- 6 z}

= - \frac{1}{6} e^{- 6 z} z - \frac{1}{36} e^{- 6 z}

Add a constant to the solution

= - \frac{1}{6} e^{- 6 z} z - \frac{1}{36} e^{- 6 z} + C

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What is the integral of z/(e^{6z)} ?
The integral of z/(e^{6z)} is -1/6 e^{-6z}z-1/36 e^{-6z}+C