Răspuns:
[tex] 3*ln\frac{5}{2}[/tex]
Explicație pas cu pas:
[tex]I=\int\limits^3_2 {(2x+1)*f(x)} \, dx =\int\limits^3_2 {(2x+1)*\frac{3}{x^2+x-2} } \, dx\\Notam~x^2+x-2=t => (2x+1) dx=dt\\Daca~x=2=>t=2^2+2-2=4.\\Daca~x=3=>t=3^2+3-2=9+3-2=10.\\I~devine:\\I=\int\limits^{10}_4 {\frac{3}{t} } \, dt=3\int\limits^{10}_4 {\frac{1}{t} } \, dt=3*lnt|^{10}_4=3(ln10-ln4)=3*ln\frac{10}{4} =3*ln\frac{5}{2}[/tex]
