Question Number 214756 by MathematicalUser2357 last updated on 19/Dec/24
$$\int\frac{\mathrm{1}}{\mathrm{2}\sqrt{{x}}}\mathrm{sin}\:\sqrt{{x}}{dx}=? \\ $$
Answered by mr W last updated on 19/Dec/24
$$=\int\mathrm{sin}\:\sqrt{{x}}\:{d}\left(\sqrt{{x}}\right) \\ $$$$=−\mathrm{cos}\:\sqrt{{x}}+{C} \\ $$
Answered by MrGaster last updated on 01/Jan/25
$$=\int\mathrm{sin}\:{u}\:{du}\left(\mathrm{let}\:{u}=\sqrt{{x}},{du}=\frac{\mathrm{1}}{\mathrm{2}\sqrt{{x}}}{dx}\right) \\ $$$$=−\mathrm{cos}\:{u}+{C} \\ $$$$=−\mathrm{cos}\sqrt{{x}}+{C} \\ $$