Question

求定积分 ∫上标e 下标1 (1+lnx/x)dx

如题，要有过程，最好详细点，谢谢。

Answer 1

∫上标e 下标1 (1+lnx/x)dx
=∫(1,e)(1+lnx)d(1+lnx)
=1/2 (1+lnx)²|(1,e)
=1/2 (2²-1)
=3/2

Answer 2

∫(1->e) ((1+lnx)/x)dx
= [lnx + (lnx)^2/2] (1->e)
= 1+ 1/2
=3/2