What is the integral of (5e^{-0.8x}) ?

The integral of (5e^{-0.8x}) is -6.25e^{-0.8x}+C

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integral of (5e^{-0.8x})

\int (5 e^{- 0.8 x}) d x

- 6.25 e^{- 0.8 x} + C

Solution steps

\int 5 e^{- 0.8 x} d x

Take the constant out:

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

= 5 \cdot \int e^{- 0.8 x} d x

Apply u-substitution

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

= 5 \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

= 5 (- \frac{1}{0.8} \cdot \int e^{u} d u)

Simplify

= 5 (- 1.25 \cdot \int e^{u} d u)

Use the common integral:

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

= 5 (- 1.25 e^{u})

Substitute back

u = - 0.8 x

= 5 (- 1.25 e^{- 0.8 x})

Simplify

= - 6.25 e^{- 0.8 x}

Add a constant to the solution

= - 6.25 e^{- 0.8 x} + C

y = 2 x e^{2 x} - e^{2 x}

\int 18 sin^{- \frac{3}{2}} (x) cos^{3} (x) d x

(x - 8 y) d x + (4 x) d y = 0

\frac{( s + 1 ) ^{3}}{s ^{5}}

x \to 5 lim (\frac{( x - 5 )}{x ^{2} + 5})

What is the integral of (5e^{-0.8x}) ?
The integral of (5e^{-0.8x}) is -6.25e^{-0.8x}+C