Integral of $$$\frac{\left(x - y\right) \left(\left(x - y\right)^{2} + \pi^{2}\right)^{2} \left(e^{x} + e^{y}\right)}{e^{4}}$$$ with respect to $$$x$$$
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Find $$$\int \frac{\left(x - y\right) \left(\left(x - y\right)^{2} + \pi^{2}\right)^{2} \left(e^{x} + e^{y}\right)}{e^{4}}\, dx$$$.