This is a test of Brilliant features

\[ I_{1}=\int_{0}^{1} x^x \; \mathrm{d}x, \\ I_{2}=\int_{0}^{1} \int_{0}^{1} (xy)^{xy} ; \mathrm{d}y \; \mathrm{d} x, \\ I_{3}=\int_{0}^{1} \int_{0}^{1} \int_{0}^{1} (xyz)^{xyz} \; \mathrm{d} z \; \mathrm{d}y \; \mathrm{d} x. \]

Which of these statements is true?

  • \( I_1 = I_2 = I_3 \)
  • \( I_1 = I_2 \neq I_3 \)
  • \( I_2 = I_3 \neq I_1 \)
  • \( I_3 = I_1 \neq I_2 \)
  • \( I_1 \neq I_2 \neq I_3 \)
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