Question Number 11621 by Nayon last updated on 29/Mar/17
$${Evaluate}\:\:\int\frac{{ax}+{b}}{{cx}+{d}}{dx} \\ $$
Answered by mrW1 last updated on 29/Mar/17
$$=\int\frac{\frac{{a}}{{c}}\left({cx}+{d}\right)+\left({b}−\frac{{ad}}{{c}}\right)}{{cx}+{d}}{dx} \\ $$$$=\frac{{a}}{{c}}\int{dx}+\left({b}−\frac{{ad}}{{c}}\right)×\frac{\mathrm{1}}{{c}}\int\frac{{d}\left({cx}+{d}\right)}{{cx}+{d}} \\ $$$$=\frac{{ax}}{{c}}+\frac{{bc}−{ad}}{{c}^{\mathrm{2}} }×\mathrm{ln}\:\left({cx}+{d}\right)+{C} \\ $$