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

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

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integral of 6e^{-6x}

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

- e^{- 6 x} + C

Solution steps

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

Apply u-substitution

: \int - \frac{1}{6} e^{u} d u

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

Use the common integral:

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

= 6 (- \frac{1}{6} e^{u})

Substitute back

u = - 6 x

= 6 (- \frac{1}{6} e^{- 6 x})

Simplify

6 (- \frac{1}{6} e^{- 6 x}) : - e^{- 6 x}

= - e^{- 6 x}

Add a constant to the solution

= - e^{- 6 x} + C

x \to 1 lim (ln (x) - ln (x - 1))

x \to 0 lim (\frac{x}{x ^{2} + y ^{2}})

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