$$\int_{0}^{1}dx \int_{x}^{1}e^\frac{x}{y} dy$$
$$\int_{0}^{1}\int_{x}^{1}e^\frac{x}{y} dy dx$$
2026-04-07 06:57:49.1775545069
Are these two integrals same or different
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Changing the order of integrations, one has $$\int_{0}^{1}dx \int_{x}^{1}e^\frac{x}{y} dy=\int_{0}^{1}dy \int_{0}^{y}e^\frac{x}{y} dx=\int_0^1y(e-1)dy=\frac12(e-1).$$