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

Take the constant out:

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

= - \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})

Simplify

= e^{- u}

Add a constant to the solution

= e^{- u} + C

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