f(x)=[tex] x^{2011}(x+1)+x(x+1)=(x+1)( x^{2011} +x)[/tex]
Integrala va fi: [tex] \int\limits^1_0 { \frac{f(x)}{x+1} } \, dx = \int\limits^1_0 ({ x^{2011}+x }) \, dx = (\frac{ x^{2012} }{2012} + \frac{ x^{2} }{2} )[/tex] cu limitele de integrare 1 si 0 deci [tex] \frac{1}{2012} + \frac{1}{2} = \frac{1007}{2012} [/tex]
