What is the integral of e^{-x/θ} ?

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

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integral of e^{-x/θ}

\int e^{- \frac{x}{θ}} d x

- θ e^{- \frac{x}{θ}} + C

Solution steps

\int e^{- \frac{x}{θ}} d x

Apply u-substitution

: \int - θ e^{u} d u

= \int - θ e^{u} d u

Take the constant out:

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

= - θ \cdot \int e^{u} d u

Use the common integral:

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

= - θ e^{u}

Substitute back

u = - \frac{x}{θ}

= - θ e^{- \frac{x}{θ}}

Add a constant to the solution

= - θ e^{- \frac{x}{θ}} + C

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