What is the integral of-9000e^{-0.075t} ?

The integral of-9000e^{-0.075t} is 119999.99999…e^{-0.075t}+C

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integral of-9000e^{-0.075t}

\int - 9000 e^{- 0.075 t} d t

119999.99999 \dots e^{- 0.075 t} + C

Solution steps

\int - 9000 e^{- 0.075 t} d t

Take the constant out:

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

= - 9000 \cdot \int e^{- 0.075 t} d t

Apply u-substitution

: \int - \frac{1}{0.075} e^{u} d u

= - 9000 \cdot \int - \frac{1}{0.075} e^{u} d u

Take the constant out:

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

= - 9000 (- \frac{1}{0.075} \cdot \int e^{u} d u)

Simplify

= - 9000 (- 13.33333 \dots \cdot \int e^{u} d u)

Use the common integral:

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

= - 9000 (- 13.33333 \dots e^{u})

Substitute back

u = - 0.075 t

= - 9000 (- 13.33333 \dots e^{- 0.075 t})

Simplify

= 119999.99999 \dots e^{- 0.075 t}

Add a constant to the solution

= 119999.99999 \dots e^{- 0.075 t} + C

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What is the integral of-9000e^{-0.075t} ?
The integral of-9000e^{-0.075t} is 119999.99999…e^{-0.075t}+C