Question Number 88494 by I want to learn more last updated on 11/Apr/20
$$\int\:\sqrt{\mathrm{cos}\left(\mathrm{x}\right)}\:\:\mathrm{dx} \\ $$
Commented by Tony Lin last updated on 11/Apr/20
$$\int\sqrt{{cosx}}{dx} \\ $$$$=\int\sqrt{\mathrm{1}−\mathrm{2}{sin}^{\mathrm{2}} \frac{{x}}{\mathrm{2}}}{dx} \\ $$$${let}\:{u}=\frac{{x}}{\mathrm{2}},\:\mathrm{2}{du}={dx} \\ $$$$\mathrm{2}\int\sqrt{\mathrm{1}−\mathrm{2}{sin}^{\mathrm{2}} {u}}{du} \\ $$$$=\mathrm{2}{E}\left({u}\mid\mathrm{2}\right)+{c} \\ $$$$=\mathrm{2}{E}\left(\frac{{x}}{\mathrm{2}}\mid\mathrm{2}\right)+{c} \\ $$
Commented by I want to learn more last updated on 11/Apr/20
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir} \\ $$