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

The integral of e^{-yx} is -1/y e^{-yx}+C

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integral of e^{-yx}

\int e^{- y x} d x

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

Solution steps

\int e^{- y x} d x

Apply u-substitution

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

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

Take the constant out:

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

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

Use the common integral:

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

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

Substitute back

u = - y x

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

Add a constant to the solution

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

\frac{d}{d x} (\frac{6 x}{x - 1})

\int y e^{x} + sin (y) d x

\int_{0}^{2} 2 x^{2} x^{3} + 1 d x

y^{^{''}} + 16 y = 24 sec (4 t)