Ma puteti ajuta la ex 2 punctul b de la Subiectul 3 va rog ?

[tex] \int\limits^1_0 { x^{2} f(x)} \, dx = \int\limits^1_0 { \frac{ x^{2} }{x+1} } \, dx= \int\limits^1_0 { \frac{ x^{2}-1+1 }{x+1} } \, dx= \int\limits^1_0 { \frac{(x-1)(x+1)+1}{x+1} } \, dx[/tex][tex] \int\limits^1_0 {x-1+ \frac{1}{x+1} } \, dx= \frac{ x^{2} }{2}-x+ln(x+1) \int\limits^1_0= \frac{1}{2}-1+ln(2)= \frac{-1}{2}+ln(2) [/tex]

[tex] \int\limits^1_0 {x^2* \frac{1}{x+1} } \, dx [/tex]

[tex] \int\limits^1_0 { \frac{x^2}{x+1} } \, dx [/tex]

[tex]ln ( | x +1|)+ \frac{x^2-2x}{2} +C[/tex]

[tex]ln ( | x +1|)+ \frac{x(x+2)}{2} +C[/tex]

[tex] \frac{2ln(2)-1}{2} [/tex]

[tex]ln(2)- \frac{1}{2} [/tex]