[tex] \int\limits^1_0 { \frac{x+1-1}{x+1} dx=[/tex]
[tex] \int\limits^1_0 { \frac{x+1}{x+1} dx - \int\limits^1_0 { \frac{1}{x+1} dx =
[/tex]
Calculam a doua integrala prin schimbare de variabila !!
[tex] \int\limits^1_0 { \frac{x}{x+1} } \, dx =
x+1=t
(x+1)`dx=t`dt
dx=dt[/tex]
x=0 >>> t=1
x=1=>> t=2
[tex] \int\limits^2_1 { \frac{1}{t} } \, dt = ln |t| = ln2-ln1=ln2[/tex]
Prima integrala >>
[tex] \int\limits^1_0 { \frac{x+1}{x+1} dx= \int\limits^1_0 { dx= x = 1[/tex]
[tex]\int\limits^1_0 { \frac{x+1}{x+1} dx - \int\limits^1_0 { \frac{1}{x+1}dx= 1-ln2[/tex]
