What is the integral of e^{-xy} ?

The integral of e^{-xy} is -1/x e^{-xy}+C

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integral of e^{-xy}

\int e^{- x y} d y

- \frac{1}{x} e^{- x y} + C

Solution steps

\int e^{- x y} d y

Apply u-substitution

: \int - \frac{e ^{u}}{x} d u

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

Take the constant out:

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

= - \frac{1}{x} \cdot \int e^{u} d u

Use the common integral:

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

= - \frac{1}{x} e^{u}

Substitute back

u = - x y

= - \frac{1}{x} e^{- x y}

Add a constant to the solution

= - \frac{1}{x} e^{- x y} + C

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\frac{d}{d x} (\frac{x ^{3}}{19})

\frac{d}{d x} (\frac{6}{x ^{- 3}})

y^{^{''}} = - 3 y - 2 y^{^{'}}