Question Number 226818 by Spillover last updated on 16/Dec/25
$${Evaluate} \\ $$$$\int\frac{{x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{1}}{\mathrm{2}{x}^{\mathrm{3}} +\mathrm{3}{x}^{\mathrm{2}} −\mathrm{2}{x}}{dx} \\ $$
Answered by Frix last updated on 16/Dec/25
$$=\frac{\mathrm{1}}{\mathrm{2}}\int\frac{{dx}}{{x}}−\frac{\mathrm{1}}{\mathrm{10}}\int\frac{{dx}}{{x}+\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{5}}\int\frac{{dx}}{\mathrm{2}{x}−\mathrm{1}}= \\ $$$$=\frac{\mathrm{1}}{\mathrm{10}}\mathrm{ln}\:\mid\frac{{x}^{\mathrm{5}} \left(\mathrm{2}{x}−\mathrm{1}\right)}{{x}+\mathrm{2}}\mid\:+{C} \\ $$
Commented by Spillover last updated on 16/Dec/25
$${thanks} \\ $$