What is the integral of e^{(-x/2)} ?

The integral of e^{(-x/2)} is -2e^{-x/2}+C

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integral of e^{(-x/2)}

\int e^{(- \frac{x}{2})} d x

- 2 e^{- \frac{x}{2}} + C

Solution steps

\int e^{- \frac{x}{2}} d x

Apply u-substitution

: \int - 2 e^{u} d u

= \int - 2 e^{u} d u

Take the constant out:

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

= - 2 \cdot \int e^{u} d u

Use the common integral:

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

= - 2 e^{u}

Substitute back

u = - \frac{x}{2}

= - 2 e^{- \frac{x}{2}}

Add a constant to the solution

= - 2 e^{- \frac{x}{2}} + C

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