What is the integral of e^{-x/4} ?

The integral of e^{-x/4} is -4e^{-x/4}+C

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integral of e^{-x/4}

\int e^{- \frac{x}{4}} d x

- 4 e^{- \frac{x}{4}} + C

Solution steps

\int e^{- \frac{x}{4}} d x

Apply u-substitution

: \int - 4 e^{u} d u

= \int - 4 e^{u} d u

Take the constant out:

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

= - 4 \cdot \int e^{u} d u

Use the common integral:

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

= - 4 e^{u}

Substitute back

u = - \frac{x}{4}

= - 4 e^{- \frac{x}{4}}

Add a constant to the solution

= - 4 e^{- \frac{x}{4}} + C

y = \frac{6 x}{x + 5}, (- 3, - 9)

x^{6} y^{^{'}} + x^{5} y = 0

\frac{d}{d x} (\frac{x}{x + 1})

y = 3 x, y = 3 x

\frac{\partial}{\partial y} (22 cos (x) y z^{2})