Răspuns:
[tex]\int\limits^1_0 {\frac{5+x^{2} }{4+x^{2} } x} =\int\limits^1_0 {\frac{4+x^{2}+1 }{4+x^{2} } } \, dx =\int\limits^1_0 {\frac{4+x^{2}}{4+x^{2}} } \, dx +\int\limits^1_0 {\frac{1}{4+x^{2}} } \, dx[/tex]
Cum:
[tex]\int\limits^1_0 {\frac{1}{x^{2} +4} } \, dx = \frac{1}{2} * (arctg(\frac{1}{2} ) - arctg(\frac{1}{2} ))[/tex]
avem :
[tex]\int\limits^1_0 {\frac{5+x^{2} }{4+x^{2} } x} = \int\limits^1_0 {} \, dx + \frac{1}{2} * arctg(\frac{1}{2} ) = 1 + \frac{1}{2} * arctg(\frac{1}{2} )[/tex]
