What is the integral of e^{-x/(0.2)} ?

The integral of e^{-x/(0.2)} is -0.2e^{-x/(0.2)}+C

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integral of e^{-x/(0.2)}

\int e^{- \frac{x}{0.2}} d x

- 0.2 e^{- \frac{x}{0.2}} + C

Solution steps

\int e^{- \frac{x}{0.2}} d x

Apply u-substitution

: \int - \frac{1}{5} e^{u} d u

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

Take the constant out:

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

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

Use the common integral:

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

= - \frac{1}{5} e^{u}

Substitute back

u = - \frac{x}{0.2}

= - \frac{1}{5} e^{- \frac{x}{0.2}}

Simplify

= - 0.2 e^{- \frac{x}{0.2}}

Add a constant to the solution

= - 0.2 e^{- \frac{x}{0.2}} + C

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What is the integral of e^{-x/(0.2)} ?
The integral of e^{-x/(0.2)} is -0.2e^{-x/(0.2)}+C