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

The integral of e^{-px} is -1/p e^{-px}+C

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integral of e^{-px}

\int e^{- p x} d x

- \frac{1}{p} e^{- p x} + C

Solution steps

\int e^{- p x} d x

Apply u-substitution

: \int - \frac{e ^{u}}{p} d u

= \int - \frac{e ^{u}}{p} d u

Take the constant out:

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

= - \frac{1}{p} \cdot \int e^{u} d u

Use the common integral:

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

= - \frac{1}{p} e^{u}

Substitute back

u = - p x

= - \frac{1}{p} e^{- p x}

Add a constant to the solution

= - \frac{1}{p} e^{- p x} + C

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