What is the integral of e^{-x/8} ?

The integral of e^{-x/8} is -8e^{-x/8}+C

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integral of e^{-x/8}

\int e^{- \frac{x}{8}} d x

- 8 e^{- \frac{x}{8}} + C

Solution steps

\int e^{- \frac{x}{8}} d x

Apply u-substitution

= \int - 8 e^{u} d u

Take the constant out:

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

= - 8 \cdot \int e^{u} d u

Use the common integral:

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

= - 8 e^{u}

Substitute back

u = - \frac{x}{8}

= - 8 e^{- \frac{x}{8}}

Add a constant to the solution

= - 8 e^{- \frac{x}{8}} + C