[m] ∫ \frac{dx}{2x^2+6x-3}= ∫ \frac{dx}{(2(x+\frac{3}{2})^2-\frac{15}{4}))}=\frac{1}{2} ∫ \frac{d(x+\frac{3}{2})}{((x+\frac{3}{2})^2-\frac{15}{4}}=\frac{1}{2}\cdot \frac{1}{2\cdot \sqrt{\frac{15}{4}}} ln |\frac{(x+\frac{3}{2}-\sqrt{\frac{15}{4}}}{(x+\frac{3}{2}+\sqrt{\frac{15}{4}}}|+C=[/m]
[m]=\frac{1}{2\cdot \sqrt{15}} ln |\frac{2x+3-\sqrt{15}}{2x+3+\sqrt{15}}|+C[/m]
Формула: