Răspuns:
[tex]\int\ {\frac{1}{x^{2}+3x+2} } \, dx= \int\ {\frac{1}{x^{2}+x+2x+2} } \, dx=\int\ {\frac{1}{x(x+1)+2(x+1)} } \, dx=\int\ {\frac{1}{(x+1)(x+2)} } \, dx=\int {(\frac{1}{x+1} -\frac{1}{x+2} )} \, dx =\int{\frac{1}{x+1}} \, dx- \int{\frac{1}{x+2}} \, dx =ln|x+1|-ln|x+2|+C=ln|\frac{x+1}{x+2}| +C[/tex]
Explicație pas cu pas:
