# 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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