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

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

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integral of e^{-x/y}

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

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

Solution steps

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

Apply u-substitution

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

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

Take the constant out:

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

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

Use the common integral:

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

= - y e^{u}

Substitute back

u = - \frac{x}{y}

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

Add a constant to the solution

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

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

f (x) = tan (x^{2})

x \to - 4 lim (\frac{x ^{2}}{4 - x})

y^{^{''}} - 2 y^{^{'}} - 3 y = 4 e^{- x}, y (0) = 4, y^{^{'}} (0) = - 1

\int \frac{x ^{2} + 8}{x ^{2}} d x