What is the integral of 75e^{-x/(50)} ?

The integral of 75e^{-x/(50)} is -3750e^{-x/(50)}+C

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integral of 75e^{-x/(50)}

\int 75 e^{- \frac{x}{50}} d x

- 3750 e^{- \frac{x}{50}} + C

Solution steps

\int 75 e^{- \frac{x}{50}} d x

Take the constant out:

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

= 75 \cdot \int e^{- \frac{x}{50}} d x

Apply u-substitution

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

= 75 \cdot \int - 50 e^{u} d u

Take the constant out:

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

= 75 (- 50 \cdot \int e^{u} d u)

Use the common integral:

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

= 75 (- 50 e^{u})

Substitute back

u = - \frac{x}{50}

= 75 (- 50 e^{- \frac{x}{50}})

Simplify

= - 3750 e^{- \frac{x}{50}}

Add a constant to the solution

= - 3750 e^{- \frac{x}{50}} + C

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What is the integral of 75e^{-x/(50)} ?
The integral of 75e^{-x/(50)} is -3750e^{-x/(50)}+C