What is the integral of 6.4e^{(-3x+6)} ?

The integral of 6.4e^{(-3x+6)} is -2.13333…e^{-3x+6}+C

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integral of 6.4e^{(-3x+6)}

\int 6.4 e^{(- 3 x + 6)} d x

- 2.13333 \dots e^{- 3 x + 6} + C

Solution steps

\int 6.4 e^{- 3 x + 6} d x

Take the constant out:

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

= 6.4 \cdot \int e^{- 3 x + 6} d x

Apply u-substitution

: \int - \frac{1}{3} e^{u} d u

= 6.4 \cdot \int - \frac{1}{3} e^{u} d u

Take the constant out:

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

= 6.4 (- \frac{1}{3} \cdot \int e^{u} d u)

Use the common integral:

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

= 6.4 (- \frac{1}{3} e^{u})

Substitute back

u = - 3 x + 6

= 6.4 (- \frac{1}{3} e^{- 3 x + 6})

Simplify

6.4 (- \frac{1}{3} e^{- 3 x + 6}) : - 2.13333 \dots e^{- 3 x + 6}

= - 2.13333 \dots e^{- 3 x + 6}

Add a constant to the solution

= - 2.13333 \dots e^{- 3 x + 6} + C

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What is the integral of 6.4e^{(-3x+6)} ?
The integral of 6.4e^{(-3x+6)} is -2.13333…e^{-3x+6}+C