Question Number 121825 by bemath last updated on 12/Nov/20
$$\:\:\int\:\frac{{dx}}{{x}−\mathrm{4}\sqrt{{x}}}\:? \\ $$
Commented by bemath last updated on 12/Nov/20
$$\:\int\:\frac{{dx}}{\:\sqrt{{x}}\:\left(\sqrt{{x}}−\mathrm{4}\right)}\:{dx}\:=\:\mathrm{2}\int\:\frac{{d}\left(\sqrt{{x}}−\mathrm{4}\right)}{\:\sqrt{{x}}−\mathrm{4}} \\ $$$$=\:\mathrm{2}\:\mathrm{ln}\:\mid\sqrt{{x}}−\mathrm{4}\:\mid\:+\:{c}\: \\ $$
Answered by Dwaipayan Shikari last updated on 12/Nov/20
$$\int\frac{{dx}}{\:\sqrt{{x}}\left(\sqrt{{x}}−\mathrm{4}\right)} \\ $$$$=\mathrm{2}\int\frac{\mathrm{1}}{\mathrm{2}\sqrt{{x}}}.\frac{\mathrm{1}}{\:\sqrt{{x}}−\mathrm{4}}{dx} \\ $$$$=\mathrm{2}{log}\left(\sqrt{{x}}−\mathrm{4}\right)+{C} \\ $$