What is the integral of e*e^{-x} ?

The integral of e*e^{-x} is -e^{1-x}+C

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integral of e*e^{-x}

\int e \cdot e^{- x} d x

- e^{1 - x} + C

Solution steps

\int e e^{- x} d x

Take the constant out:

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

= e \cdot \int e^{- x} d x

Apply u-substitution

= e \cdot \int - e^{u} d u

Take the constant out:

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

= e (- \int e^{u} d u)

Use the common integral:

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

= e (- e^{u})

Substitute back

u = - x

= e (- e^{- x})

Simplify

e (- e^{- x}) : - e^{1 - x}

= - e^{1 - x}

Add a constant to the solution

= - e^{1 - x} + C

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