What is the integral of 5/(e^{-x)} ?

The integral of 5/(e^{-x)} is 5e^x+C

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integral of 5/(e^{-x)}

\int \frac{5}{e ^{- x}} d x

5 e^{x} + C

Solution steps

\int \frac{5}{e ^{- x}} d x

Take the constant out:

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

= 5 \cdot \int \frac{1}{e ^{- x}} d x

Simplify

\frac{1}{e ^{- x}} : e^{x}

= 5 \cdot \int e^{x} d x

Use the common integral:

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

= 5 e^{x}

Add a constant to the solution

= 5 e^{x} + C

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