在帮忙做一题咯,亲∫上面是e下面是12x²㏑xdx

Question

在帮忙做一题咯,亲∫上面是e下面是1 2x²㏑xdx

Answer 1

不好意思,刚刚出去了,才回来.
∫(1→e) 2x²lnx dx
= ∫(1→e) lnx d(2x³/3)
= (2/3)x³lnx |(1→e) - (2/3)∫(1→e) x³ d(lnx),分部积分法
= (2/3)(e³ - 0) - (2/3)∫(1→e) x³ * 1/x dx
= (2/3)e³ - (2/3) * x³/3 |(1→e)
= (2/3)e³ - (2/9)(e³ - 1)
= 2(2e³ + 1)/9