What is the integral of z/(e^{7z)} ?

The integral of z/(e^{7z)} is -1/7 e^{-7z}z-1/49 e^{-7z}+C

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integral of z/(e^{7z)}

\int \frac{z}{e ^{7 z}} d z

- \frac{1}{7} e^{- 7 z} z - \frac{1}{49} e^{- 7 z} + C

Solution steps

\int \frac{z}{e ^{7 z}} d z

Apply Integration By Parts

: - \frac{1}{7} e^{- 7 z} z - \int - \frac{1}{7} e^{- 7 z} d z

= - \frac{1}{7} e^{- 7 z} z - \int - \frac{1}{7} e^{- 7 z} d z

\int - \frac{1}{7} e^{- 7 z} d z = \frac{1}{49} e^{- 7 z}

= - \frac{1}{7} e^{- 7 z} z - \frac{1}{49} e^{- 7 z}

Add a constant to the solution

= - \frac{1}{7} e^{- 7 z} z - \frac{1}{49} e^{- 7 z} + C

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What is the integral of z/(e^{7z)} ?
The integral of z/(e^{7z)} is -1/7 e^{-7z}z-1/49 e^{-7z}+C