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The integral $\int\frac{e^y}{y}dy$ is called 'exponential integral' and is non-elementary. The formula for the exponential integral is: $\int\frac{e^x}{x}=Ei(x)$, where $Ei$ is a special function on the complex plane
As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration $C$