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

Simplify

= \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

x \to \frac{5 π}{6} lim (cos (x))

\frac{d}{d y} (\frac{x}{y ^{2}})

n = 1 \sum \infty \frac{5}{n ( n + 6 )}

2 x^{2} + 3 x y + 1 y^{3} = - 10, (- 3, - 4)

x^{2} y^{^{''}} + x y^{^{'}} + y = sec (ln (x))