What is the integral of se^{-sxy} ?

The integral of se^{-sxy} is -(e^{-syx})/y+C

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integral of se^{-sxy}

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

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

Solution steps

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

Take the constant out:

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

= s \cdot \int e^{- sy x} d x

Apply u-substitution

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

= s \cdot \int - \frac{e ^{u}}{sy} d u

Take the constant out:

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

= s (- \frac{1}{sy} \cdot \int e^{u} d u)

Use the common integral:

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

= s (- \frac{1}{sy} e^{u})

Substitute back

u = - sy x

= s (- \frac{1}{sy} e^{- sy x})

Simplify

s (- \frac{1}{sy} e^{- sy x}) : - \frac{e ^{- sy x}}{y}

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

Add a constant to the solution

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

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What is the integral of se^{-sxy} ?
The integral of se^{-sxy} is -(e^{-syx})/y+C