Verified answer

u = ln x , dv = x dx --> answer is (x² / 2 ) ln x - x² / 4...

evaluate at x = 7 , take away the value at x = 0 ; { 24.5 ln 7 - 12.25 } - { 0 - 0 }

x² ln x ---> 0 as x---> 0...look at ln x / [ 1 / x² ]..use LH on this

∫xlnxdx on [0,7]

= (1/2)x^2lnx - (1/2)∫x^2/xdx on [0,7]

= (1/2)x^2lnx - (1/4)x^2 on [0, 7]

= (1/2)49ln7 - 49/4

----------

Attn: lim{x->0} x^2lnx = lim{y->inf} -lny / y^2 = lim{y->inf} -1/[y(2y)] = 0