What is the integral of-18e^{-0.6x} ?

The integral of-18e^{-0.6x} is 30.00000…e^{-0.6x}+C

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integral of-18e^{-0.6x}

\int - 18 e^{- 0.6 x} d x

30.00000 \dots e^{- 0.6 x} + C

Solution steps

\int - 18 e^{- 0.6 x} d x

Take the constant out:

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

= - 18 \cdot \int e^{- 0.6 x} d x

Apply u-substitution

: \int - \frac{1}{0.6} e^{u} d u

= - 18 \cdot \int - \frac{1}{0.6} e^{u} d u

Take the constant out:

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

= - 18 (- \frac{1}{0.6} \cdot \int e^{u} d u)

Simplify

= - 18 (- 1.66666 \dots \cdot \int e^{u} d u)

Use the common integral:

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

= - 18 (- 1.66666 \dots e^{u})

Substitute back

u = - 0.6 x

= - 18 (- 1.66666 \dots e^{- 0.6 x})

Simplify

= 30.00000 \dots e^{- 0.6 x}

Add a constant to the solution

= 30.00000 \dots e^{- 0.6 x} + C

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What is the integral of-18e^{-0.6x} ?
The integral of-18e^{-0.6x} is 30.00000…e^{-0.6x}+C