Question Number 207130 by hardmath last updated on 07/May/24
$$\mathrm{Find}:\:\:\:\int\:\frac{\mathrm{x}\:−\:\mathrm{1}}{\mathrm{x}\:−\:\mathrm{2}}\:\mathrm{dx}\:\:=\:\:? \\ $$
Answered by Frix last updated on 07/May/24
$$\int\frac{{x}\pm{a}}{{x}\pm{b}}{dx}=\int{dx}+\left(\pm{a}\mp{b}\right)\int\frac{{dx}}{{x}\pm{b}}= \\ $$$$={x}+\left(\pm{a}\mp{b}\right)\mathrm{ln}\:\mid{x}\pm{b}\mid\:+{C} \\ $$
Commented by hardmath last updated on 07/May/24
$$\mathrm{thank}\:\mathrm{you}\:\mathrm{dear}\:\mathrm{professor} \\ $$$$\mathrm{x}+\mathrm{ln}\mid\mathrm{x}−\mathrm{2}\mid+\mathrm{C} \\ $$
Commented by Frix last updated on 07/May/24
����