Question Number 188035 by Michaelfaraday last updated on 25/Feb/23
$${solve} \\ $$$$\int\frac{{x}^{\mathrm{2}} }{\left({a}+{bx}\right)^{\mathrm{2}} }{dx} \\ $$
Answered by MJS_new last updated on 25/Feb/23
$$\int\frac{{x}^{\mathrm{2}} }{\left({a}+{bx}\right)^{\mathrm{2}} }{dx}= \\ $$$$=\frac{\mathrm{1}}{{b}^{\mathrm{2}} }\int{dx}−\frac{\mathrm{2}{a}}{{b}^{\mathrm{2}} }\int\frac{{dx}}{{a}+{bx}}+\frac{{a}^{\mathrm{2}} }{{b}^{\mathrm{2}} }\int\frac{{dx}}{\left({a}+{bx}\right)^{\mathrm{2}} }= \\ $$$$=\frac{{x}}{{b}^{\mathrm{2}} }−\frac{{a}^{\mathrm{2}} }{{b}^{\mathrm{3}} \left({a}+{bx}\right)}−\frac{\mathrm{2}{a}}{{b}^{\mathrm{3}} }\mathrm{ln}\:\mid{a}+{bx}\mid\:+{C} \\ $$
Commented by Michaelfaraday last updated on 01/Mar/23
$${thanks}\:{sir} \\ $$