Question Number 206558 by luciferit last updated on 18/Apr/24
Answered by Frix last updated on 18/Apr/24
$$\int\sqrt{\mathrm{3}+\mathrm{5}\sqrt{{x}}}{dx}\:\overset{{t}=\sqrt{\mathrm{3}+\mathrm{5}\sqrt{{x}}}} {=}\: \\ $$$$=\frac{\mathrm{4}}{\mathrm{25}}\int\left({t}^{\mathrm{4}} −\mathrm{3}{t}^{\mathrm{2}} \right){dt}=\frac{\mathrm{4}}{\mathrm{25}}\left(\frac{{t}^{\mathrm{5}} }{\mathrm{5}}−{t}^{\mathrm{3}} \right)= \\ $$$$=\frac{\mathrm{4}\left(\mathrm{25}{x}+\mathrm{5}\sqrt{{x}}−\mathrm{6}\right)\sqrt{\mathrm{3}+\mathrm{5}\sqrt{{x}}}}{\mathrm{125}}+{C} \\ $$