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

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

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integral of u/(e^u)

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

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