What is the integral of e^{-u} ?

The integral of e^{-u} is -e^{-u}+C

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integral of e^{-u}

\int e^{- u} d u

- e^{- u} + C

Solution steps

\int e^{- u} d u

Apply u-substitution

: \int - e^{v} d v

= \int - e^{v} d v

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int e^{v} d v

Use the common integral:

\int e^{v} d v = e^{v}

= - e^{v}

Substitute back

v = - u

= - e^{- u}

Add a constant to the solution

= - e^{- u} + C

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