Question Number 64463 by aliesam last updated on 18/Jul/19
$$\int\sqrt{{sec}\left({x}\right)}\:{dx} \\ $$
Commented by Tony Lin last updated on 18/Jul/19
$$\int\sqrt{{secx}}{dx} \\ $$$$=\int\frac{{dx}}{\:\sqrt{{cosx}}}\: \\ $$$$=\int\frac{{dx}}{\:\sqrt{\mathrm{1}−\mathrm{2}{sin}^{\mathrm{2}} \frac{{x}}{\mathrm{2}}}} \\ $$$$={F}\left(\frac{{x}}{\mathrm{2}}\mid\mathrm{2}\right)+{c} \\ $$$$={F}\left(\frac{{x}}{\mathrm{2}},\sqrt{\mathrm{2}}\right)+{c} \\ $$$$\left({incomplete}\:{elliptic}\:{integral}\:{of}\right. \\ $$$$\left.{the}\:{first}\:{kind}\right) \\ $$