∫(0->1/e) ln(1+x) dx
= [xln(1+x)](0->1/e) - ∫(0->1/e) [x/(1+x)] dx
=(1/e)[ ln(e+1) - 1] - ∫(0->1/e) dx + ∫(0->1/e) dx/(1+x)
=(1/e)[ ln(e+1) - 1] - [x](0->1/e) + [ln(1+x)](0->1/e)
=(1/e)[ ln(e+1) - 1] - 1/e + (ln(e+1) - 1)
= {[ ln(e+1) - 1] ( e+1) - 1}/e