What is the integral of 14e^{-14x} ?

The integral of 14e^{-14x} is -e^{-14x}+C

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integral of 14e^{-14x}

\int 14 e^{- 14 x} d x

- e^{- 14 x} + C

Solution steps

\int 14 e^{- 14 x} d x

Take the constant out:

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

= 14 \cdot \int e^{- 14 x} d x

Apply u-substitution

: \int - \frac{1}{14} e^{u} d u

= 14 \cdot \int - \frac{1}{14} e^{u} d u

Take the constant out:

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

= 14 (- \frac{1}{14} \cdot \int e^{u} d u)

Use the common integral:

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

= 14 (- \frac{1}{14} e^{u})

Substitute back

u = - 14 x

= 14 (- \frac{1}{14} e^{- 14 x})

Simplify

14 (- \frac{1}{14} e^{- 14 x}) : - e^{- 14 x}

= - e^{- 14 x}

Add a constant to the solution

= - e^{- 14 x} + C

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