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

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

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

Simplify

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

Apply u-substitution

= \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

y^{^{'}} = \frac{y}{x} + tan (\frac{y}{x})

4 y^{^{''}} + 9 y = 0, y (0) = 2, y^{^{'}} (0) = 3

\frac{d}{d x} (a (2 e^{- 3 x} x - 3 e^{- 3 x} x^{2}))

\frac{\partial}{\partial x} (- sin (4 x))

d er i v a t i v e f (x) = x^{2} + 2 x + 3

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