What is the integral of e^{-x/(50)} ?

The integral of e^{-x/(50)} is -50e^{-x/(50)}+C

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integral of e^{-x/(50)}

\int e^{- \frac{x}{50}} d x

- 50 e^{- \frac{x}{50}} + C

Solution steps

\int e^{- \frac{x}{50}} d x

Apply u-substitution

: \int - 50 e^{u} d u

= \int - 50 e^{u} d u

Take the constant out:

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

= - 50 \cdot \int e^{u} d u

Use the common integral:

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

= - 50 e^{u}

Substitute back

u = - \frac{x}{50}

= - 50 e^{- \frac{x}{50}}

Add a constant to the solution

= - 50 e^{- \frac{x}{50}} + C

y^{^{''}} + 20 y^{^{'}} + 200 y = 150

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What is the integral of e^{-x/(50)} ?
The integral of e^{-x/(50)} is -50e^{-x/(50)}+C