What is the integral of (5e^{-0.4x}) ?

The integral of (5e^{-0.4x}) is -12.5e^{-0.4x}+C

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integral of (5e^{-0.4x})

\int (5 e^{- 0.4 x}) d x

- 12.5 e^{- 0.4 x} + C

Solution steps

\int 5 e^{- 0.4 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^{- 0.4 x} d x

Apply u-substitution

= 5 \cdot \int - \frac{1}{0.4} 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}{0.4} \cdot \int e^{u} d u)

Simplify

= 5 (- 2.5 \cdot \int e^{u} d u)

Use the common integral:

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

= 5 (- 2.5 e^{u})

Substitute back

u = - 0.4 x

= 5 (- 2.5 e^{- 0.4 x})

Simplify

= - 12.5 e^{- 0.4 x}

Add a constant to the solution

= - 12.5 e^{- 0.4 x} + C

What is the integral of (5e^{-0.4x}) ?
The integral of (5e^{-0.4x}) is -12.5e^{-0.4x}+C