Question Number 89362 by cindiaulia last updated on 17/Apr/20
$$\int\frac{\mathrm{1}}{\:\sqrt{\mathrm{x}}\left(\sqrt{\mathrm{x}}+\mathrm{1}\right)^{\mathrm{3}} } \\ $$
Commented by jagoll last updated on 17/Apr/20
$${u}\:=\:\mathrm{1}+\sqrt{{x}}\:\Rightarrow\:{du}\:=\:\frac{{dx}}{\mathrm{2}\sqrt{{x}}}\: \\ $$$$\int\:\frac{\mathrm{2}\:{du}}{{u}^{\mathrm{3}} }\:=\:\int\:\mathrm{2}{u}^{−\mathrm{3}} \:{du}\:=\:−{u}^{−\mathrm{2}} \:+\:{c} \\ $$$$=\:−\frac{\mathrm{1}}{\left(\sqrt{{x}}+\mathrm{1}\right)^{\mathrm{2}} }\:+\:{c}\: \\ $$