Table of Integrals, Series, and Products, 8th Edition

$\begin{array}{r}\hfill {\displaystyle {\int }_u^c\sqrt{\frac{\left(a-x\right)\left(b-x\right)}{c-x}}\text{d}x=\frac{2}{3}\sqrt{a-c}\left[2\left(b-c\right)F\left(\beta ,p\right)+\left(2c-a-b\right)E\left(\beta ,p\right)\right]}\\ \hfill +\frac{2}{3}\left(a+2b-2c-u\right)\sqrt{\frac{\left(a-u\right)\left(c-u\right)}{b-u}}\end{array}$

  BY (232.09)

$\left[a>b>c>u\right]$

32. 

$\begin{array}{r}\hfill {\displaystyle {\int }_c^u\sqrt{\frac{\left(a-x\right)\left(b-x\right)}{c-x}}\text{d}x=\frac{2}{3}\sqrt{a-c}\left[\left(a+b-2c\right)E\left(\gamma ,q\right)-\left(a-b\right)F\left(\gamma ,q\right)\right]}\\ \hfill +\frac{2}{3}\sqrt{\left(a-c\right)\left(b-u\right)\left(u-c\right)}\end{array}$

  BY (233.07)

$\left[a>b\ge u>c\right]$

33. 

$\begin{array}{r}\hfill {\displaystyle {\int }_u^b\sqrt{\frac{\left(a-x\right)\left(b-x\right)}{c-x}}\text{d}x=\frac{2}{3}\sqrt{a-c}\left[\left(a+b-2c\right)E\left(\delta ,q\right)-\left(a-b\right)F\left(\delta ,q\right)\right]}\\ \hfill +\frac{2}{3}\left(2c-2a-b+u\right)\sqrt{\frac{\left(b-u\right)\left(u-c\right)}{a-u}}\end{array}$

  BY (234.09)

$\left[a>b\ge u>c\right]$

34. 

$\begin{array}{l}{\displaystyle {\int }_b^u\sqrt{\frac{\left(a-x\right)\left(x-b\right)}{x-c}}\text{d}x=\frac{2}{3}\sqrt{a-c}[}\hfill \end{array}$