Conditii impuse pentru logaritmi x>0 si x+1>0
I=∫(x+2)[ln(x+1)-lnx]dx=∫(x+2)[ln(x+1)/x]dx=(x+2)²/2*ln(x+1)/x-1/2∫(x+2)²*(x-x)*x/(x+1) dx=(x+2)²/2*ln(x+1)/x de la 0 la 1
tinad cont de limitele de integrare obtinem
I=9ln2/2
am aplicat ;ln(u(x)]'=u'/u unde u=(x+1)/x=[(x-x)*/x²]/ [x/(x+1)]=0
