What is the integral of 1/6 e^{-x/6} ?

The integral of 1/6 e^{-x/6} is -e^{-x/6}+C

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integral of 1/6 e^{-x/6}

\int \frac{1}{6} e^{- \frac{x}{6}} d x

- e^{- \frac{x}{6}} + C

Solution steps

\int \frac{1}{6} e^{- \frac{x}{6}} d x

Take the constant out:

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

= \frac{1}{6} \cdot \int e^{- \frac{x}{6}} d x

Apply u-substitution

: \int - 6 e^{u} d u

= \frac{1}{6} \cdot \int - 6 e^{u} d u

Take the constant out:

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

= \frac{1}{6} (- 6 \cdot \int e^{u} d u)

Use the common integral:

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

= \frac{1}{6} (- 6 e^{u})

Substitute back

u = - \frac{x}{6}

= \frac{1}{6} (- 6 e^{- \frac{x}{6}})

Simplify

\frac{1}{6} (- 6 e^{- \frac{x}{6}}) : - e^{- \frac{x}{6}}

= - e^{- \frac{x}{6}}

Add a constant to the solution

= - e^{- \frac{x}{6}} + C

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What is the integral of 1/6 e^{-x/6} ?
The integral of 1/6 e^{-x/6} is -e^{-x/6}+C