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

The integral of e^{-0.8x} is -1.25e^{-0.8x}+C

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integral of e^{-0.8x}

\int e^{- 0.8 x} d x

- 1.25 e^{- 0.8 x} + C

Solution steps

\int e^{- 0.8 x} d x

Apply u-substitution

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

= \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

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

Simplify

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

Use the common integral:

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

= - 1.25 e^{u}

Substitute back

u = - 0.8 x

= - 1.25 e^{- 0.8 x}

Add a constant to the solution

= - 1.25 e^{- 0.8 x} + C

\frac{\partial}{\partial x} (x^{2} \cdot ln (y))

\frac{d}{d x} (sin (2 x - \frac{π}{3}))

\frac{\partial}{\partial x} (x^{3} + y^{2} - y x^{2} - x y)

\frac{d}{d t} (5 e^{t} cos (t))

f (x) = cos (5 x)

What is the integral of e^{-0.8x} ?
The integral of e^{-0.8x} is -1.25e^{-0.8x}+C