∫(1→e²) xlnx dx
= ∫(1→e²) lnx d(x²/2),分部积分
= (1/2)x²lnx |(1→e²) - (1/2)∫(1→e²) x² d(lnx)
= (1/2)[e⁴ • 2 - 0] - (1/2)∫(1→e²) x² • 1/x dx
= e⁴ - (1/2)[x²/2] |(1→e²)
= e⁴ - (1/4)[e⁴ - 1]
= 1/4 + 3e⁴/4
= (1 + 3e⁴)/4