Question Number 186048 by ARUNG_Brandon_MBU last updated on 31/Jan/23
$$\int_{{a}} ^{{b}} \frac{{dx}}{\:\sqrt{{b}−{x}}+\sqrt{{x}−{a}}} \\ $$
Commented by ARUNG_Brandon_MBU last updated on 31/Jan/23
$$\neq\mathrm{0} \\ $$
Commented by MJS_new last updated on 31/Jan/23
$$\mathrm{sorry}\:\mathrm{I}'\mathrm{ve}\:\mathrm{not}\:\mathrm{got}\:\mathrm{enough}\:\mathrm{time}\:\mathrm{right}\:\mathrm{now} \\ $$$$\underset{{a}} {\overset{{b}} {\int}}...=\mathrm{2}\underset{{a}} {\overset{\left({a}+{b}\right)/\mathrm{2}} {\int}}... \\ $$$$\mathrm{solve}\:\mathrm{in}\:\mathrm{2}\:\mathrm{steps}: \\ $$$${t}=\sqrt{{b}−{x}}+\sqrt{{x}−{a}} \\ $$$${u}=\mathrm{arcsin}\:\frac{\sqrt{\mathrm{2}}{t}}{\mathrm{2}\sqrt{{b}−{a}}} \\ $$$$\mathrm{I}\:\mathrm{get} \\ $$$$\mathrm{2}\sqrt{{b}−{a}}+\sqrt{\mathrm{2}\left({b}−{a}\right)}\mathrm{ln}\:\left(−\mathrm{1}+\sqrt{\mathrm{2}}\right) \\ $$