定积分习题求1/e到e区间∫ |ln^3X / X|dX

∫[1/e---->e] |ln³x/x| dx
=∫[1/e---->1] |ln³x/x| dx+∫[1---->e] |ln³x/x| dx
=-∫[1/e---->1] ln³x/x dx+∫[1---->e] ln³x/x dx
=-∫[1/e---->1] ln³x d(lnx)+∫[1---->e] ln³x d(lnx)
=-(1/4)ln⁴x |[1/e---->1] + (1/4)ln⁴x |[1---->e]
=1/4+1/4
=1/2

答案见插入的图片