求定积分int^e_{1}{xlnxdx}的值.

Question

如题所述

Answer 1

可以采用分部积分法来求解定积分，求得的结果为1/4(e²+1)，详细过程请见图片

Answer 2

∫[1, e] xlnx dx
= ∫[1, e] (1/2)lnx dx^2
= (1/2)x^2 lnx - (1/2)∫[1, e] x dx
= (1/2) e^2 - (1/4)(e^2-1)
= (1/4)e^2 + 1