What is the integral of ce^{-x} ?

The integral of ce^{-x} is -ce^{-x}+C

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integral of ce^{-x}

\int c e^{- x} d x

- c e^{- x} + C

Solution steps

\int c e^{- x} d x

Take the constant out:

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

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

Apply u-substitution

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

Take the constant out:

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

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

Use the common integral:

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

= c (- e^{u})

Substitute back

u = - x

= c (- e^{- x})

Simplify

= - c e^{- x}

Add a constant to the solution

= - c e^{- x} + C

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