What is the integral of 6e^{-0.8x} ?

The integral of 6e^{-0.8x} is -7.5e^{-0.8x}+C

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integral of 6e^{-0.8x}

\int 6 e^{- 0.8 x} d x

- 7.5 e^{- 0.8 x} + C

Solution steps

\int 6 e^{- 0.8 x} d x

Take the constant out:

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

= 6 \cdot \int e^{- 0.8 x} d x

Apply u-substitution

: \int - \frac{1}{0.8} e^{u} d u

= 6 \cdot \int - \frac{1}{0.8} e^{u} d u

Take the constant out:

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

= 6 (- \frac{1}{0.8} \cdot \int e^{u} d u)

Simplify

= 6 (- 1.25 \cdot \int e^{u} d u)

Use the common integral:

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

= 6 (- 1.25 e^{u})

Substitute back

u = - 0.8 x

= 6 (- 1.25 e^{- 0.8 x})

Simplify

= - 7.5 e^{- 0.8 x}

Add a constant to the solution

= - 7.5 e^{- 0.8 x} + C

n = 1 \sum \infty (\frac{π}{4})^{n}

\frac{d}{d x} (4 x^{2} - 5 x + 3)

\int x - x^{2} d x

\frac{d}{d x} (x^{3} + 2 x + 3)

f (x) = 4 x^{2} + 9 x

What is the integral of 6e^{-0.8x} ?
The integral of 6e^{-0.8x} is -7.5e^{-0.8x}+C