What is the integral of (e^{xy})/(y^2) ?

The integral of (e^{xy})/(y^2) is -(e^{xy})/y+x\Ei(xy)+C

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integral of (e^{xy})/(y^2)

\int \frac{e ^{x y}}{y ^{2}} d y

- \frac{e ^{x y}}{y} + x Ei (x y) + C

Solution steps

\int \frac{e ^{x y}}{y ^{2}} d y

\frac{e ^{x y}}{y ^{2}} = e^{x y} \frac{1}{y ^{2}}

= \int e^{x y} \frac{1}{y ^{2}} d y

Apply Integration By Parts

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

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

\int - \frac{x e ^{x y}}{y} d y = - x Ei (x y)

= - \frac{e ^{x y}}{y} - (- x Ei (x y))

Simplify

= - \frac{e ^{x y}}{y} + x Ei (x y)

Add a constant to the solution

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

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What is the integral of (e^{xy})/(y^2) ?
The integral of (e^{xy})/(y^2) is -(e^{xy})/y+x\Ei(xy)+C