Question Number 221831 by Nicholas666 last updated on 11/Jun/25
$$\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\:\:\frac{\sqrt{{x}}}{\:\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\:+\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}\:{dx} \\ $$$$ \\ $$
Answered by MathematicalUser2357 last updated on 25/Jun/25
$$\frac{\mathrm{1}}{\:\sqrt{{x}}}\left(\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }−\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}+\mathrm{2}\sqrt{{kx}}{E}\left(\mathrm{sin}^{−\mathrm{1}} \left(\frac{\sqrt{\mathrm{1}−{ix}}}{\:\sqrt{\mathrm{2}}}\right)\:\underline{\vdots}\underbrace{ }\mathrm{1}\right.\right. \\ $$
Commented by Nicholas666 last updated on 28/Jun/25
$$\:\mathrm{please}\:\mathrm{proof}\:\mathrm{it} \\ $$