What is the integral of 4.4e^{(-3x+4)} ?

The integral of 4.4e^{(-3x+4)} is -1.46666…e^{-3x+4}+C

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integral of 4.4e^{(-3x+4)}

\int 4.4 e^{(- 3 x + 4)} d x

- 1.46666 \dots e^{- 3 x + 4} + C

Solution steps

\int 4.4 e^{- 3 x + 4} d x

Take the constant out:

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

= 4.4 \cdot \int e^{- 3 x + 4} d x

Apply u-substitution

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

= 4.4 \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

= 4.4 (- \frac{1}{3} \cdot \int e^{u} d u)

Use the common integral:

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

= 4.4 (- \frac{1}{3} e^{u})

Substitute back

u = - 3 x + 4

= 4.4 (- \frac{1}{3} e^{- 3 x + 4})

Simplify

4.4 (- \frac{1}{3} e^{- 3 x + 4}) : - 1.46666 \dots e^{- 3 x + 4}

= - 1.46666 \dots e^{- 3 x + 4}

Add a constant to the solution

= - 1.46666 \dots e^{- 3 x + 4} + C

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What is the integral of 4.4e^{(-3x+4)} ?
The integral of 4.4e^{(-3x+4)} is -1.46666…e^{-3x+4}+C