a-b-dx-b-x-x-a-

Question Number 186048 by ARUNG_Brandon_MBU last updated on 31/Jan/23

\int_{a}^{b} \frac{d x}{\sqrt{b - x} + \sqrt{x - a}}

Commented by ARUNG_Brandon_MBU last updated on 31/Jan/23

\neq 0

Commented by MJS_new last updated on 31/Jan/23

sorry I^{'} ve not got enough time right now

\underset{a}{\int^{b}} \dots = 2 \underset{a}{\int^{(a + b) / 2}} \dots

solve in 2 steps :

t = \sqrt{b - x} + \sqrt{x - a}

u = \arcsin \frac{\sqrt{2} t}{2 \sqrt{b - a}}

I get

2 \sqrt{b - a} + \sqrt{2 (b - a)} \ln (- 1 + \sqrt{2})

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