Question Number 59807 by aliesam last updated on 15/May/19
$$\int\frac{{x}−\mathrm{1}}{\sqrt{\mathrm{2}{x}−{x}^{\mathrm{2}} }}\:{dx} \\ $$
Answered by tanmay last updated on 15/May/19
$${t}^{\mathrm{2}} =\mathrm{2}{x}−{x}^{\mathrm{2}} \\ $$$$\mathrm{2}{tdt}=\left(\mathrm{2}−\mathrm{2}{x}\right){dx} \\ $$$${tdt}=\left(\mathrm{1}−{x}\right){dx} \\ $$$$−{tdt}=\left({x}−\mathrm{1}\right){dx} \\ $$$$\int\frac{−{tdt}}{{t}} \\ $$$$=−{t}+{c} \\ $$$$=\left(−\mathrm{1}\right)\left(\mathrm{2}{x}−{x}^{\mathrm{2}} \right)^{\frac{\mathrm{1}}{\mathrm{2}}} +{c} \\ $$