Question Number 215404 by ajfour last updated on 05/Jan/25
$$\int_{{a}} ^{\:\:{x}} \:\frac{\sqrt{\mathrm{1}+\mathrm{4}{x}^{\mathrm{2}} }}{\:\sqrt{{a}^{\mathrm{2}} −{x}^{\mathrm{2}} }}{dx}\:=\:? \\ $$
Answered by Ghisom last updated on 06/Jan/25
$$\int\frac{\sqrt{\mathrm{1}+\mathrm{4}{x}^{\mathrm{2}} }}{\:\sqrt{{a}^{\mathrm{2}} −{x}^{\mathrm{2}} }}{dx}=\mathrm{E}\:\left(\mathrm{arcsin}\:\frac{{x}}{{a}}\mid−\mathrm{4}{a}^{\mathrm{2}} \right)\:+{C} \\ $$
Commented by ajfour last updated on 07/Jan/25
$${Thanks}.\:{Elliptic}? \\ $$
Commented by Ghisom last updated on 07/Jan/25
$$\mathrm{yes} \\ $$