What is the integral of e^{-x/(10)} ?

The integral of e^{-x/(10)} is -10e^{-x/(10)}+C

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integral of e^{-x/(10)}

\int e^{- \frac{x}{10}} d x

- 10 e^{- \frac{x}{10}} + C

Solution steps

\int e^{- \frac{x}{10}} d x

Apply u-substitution

: \int - 10 e^{u} d u

= \int - 10 e^{u} d u

Take the constant out:

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

= - 10 \cdot \int e^{u} d u

Use the common integral:

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

= - 10 e^{u}

Substitute back

u = - \frac{x}{10}

= - 10 e^{- \frac{x}{10}}

Add a constant to the solution

= - 10 e^{- \frac{x}{10}} + C

\frac{d}{d x} (20 - 2 x)

\frac{d}{d x} (\frac{x ^{4}}{8} ln (x) - \frac{x ^{4}}{32})

y = \frac{8}{x + 1}

x \to 0 lim (x \cdot e^{\frac{1}{x}})

y = (x^{4} - 6 x) e^{x}

What is the integral of e^{-x/(10)} ?
The integral of e^{-x/(10)} is -10e^{-x/(10)}+C