Integral of $$$e^{\frac{1}{x}}$$$ with respect to $$$y$$$

The calculator will find the integral/antiderivative of $$$e^{\frac{1}{x}}$$$ with respect to $$$y$$$, with steps shown.

Find $$$\int e^{\frac{1}{x}}\, dy$$$.

Apply the constant rule $$$\int c\, dy = c y$$$ with $$$c=e^{\frac{1}{x}}$$$:

$${\color{red}{\int{e^{\frac{1}{x}} d y}}} = {\color{red}{y e^{\frac{1}{x}}}}$$

Therefore,

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

Add the constant of integration:

$$\int{e^{\frac{1}{x}} d y} = y e^{\frac{1}{x}}+C$$

$$$\int e^{\frac{1}{x}}\, dy = y e^{\frac{1}{x}} + C$$$A