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

The integral of integral of e^{x/y} is Cy+1/2 e^{x/y}y^2+(xe^{x/y}y)/2-x x/2 \Ei(x/y)+C

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integral of integral of e^{x/y}

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

C y + \frac{1}{2} e^{\frac{x}{y}} y^{2} + \frac{x e ^{\frac{x}{y}} y}{2} - x \frac{x}{2} Ei (\frac{x}{y}) + C

Solution steps

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

\int e^{\frac{x}{y}} d x = y e^{\frac{x}{y}} + C

= \int (y e^{\frac{x}{y}} + C) d y

\int (y e^{\frac{x}{y}} + C) d y = C y + \frac{1}{2} e^{\frac{x}{y}} y^{2} + \frac{x e ^{\frac{x}{y}} y}{2} - x \frac{x}{2} Ei (\frac{x}{y}) + C

= C y + \frac{1}{2} e^{\frac{x}{y}} y^{2} + \frac{x e ^{\frac{x}{y}} y}{2} - x \frac{x}{2} Ei (\frac{x}{y}) + C

What is the integral of integral of e^{x/y} ?
The integral of integral of e^{x/y} is Cy+1/2 e^{x/y}y^2+(xe^{x/y}y)/2-x x/2 \Ei(x/y)+C