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∫ xlnx dx = ∫ lnx d(x²/2)
= (1/2)x²lnx - (1/2)∫ x² d(lnx)
= (1/2)x²lnx - (1/2)∫ x dx
= (1/2)x²lnx - (1/2)(x²/2) + C
= (1/2)x²lnx - (1/4)x² + C
= (1/2)x²lnx - (1/2)∫ x² d(lnx)
= (1/2)x²lnx - (1/2)∫ x dx
= (1/2)x²lnx - (1/2)(x²/2) + C
= (1/2)x²lnx - (1/4)x² + C
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