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

$\begin{array}{ll}{\displaystyle {\int }_u^b\frac{\text{d}x}{\sqrt{\left(a-x\right)\left(b-x\right){\left(x-c\right)}^5}}}\hfill & =\frac{2}{3{\left(b-c\right)}^2\sqrt{{\left(a-c\right)}^3}}\left[\left(2a+b-3c\right)F\left(\delta ,q\right)\left(a+b-2c\right)E\left(\delta ,q\right)\right]\hfill \\ +\frac{2\left[ab-3ac-2bc+4c^2+u\left(2a+b-3c\right)\right]}{3{\left(b-c\right)}^2\left(a-c\right)}\sqrt{\frac{b-u}{\left(a-u\right){\left(u-c\right)}^3}}\hfill \end{array}$

  BY (234.04)

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

15. 

$\begin{array}{ll}{\displaystyle {\int }_b^u\frac{\text{d}x}{\sqrt{\left(a-x\right)\left(x-b\right){\left(x-c\right)}^5}}}\hfill & =\frac{2}{3{\left(b-c\right)}^2\sqrt{{\left(a-c\right)}^3}}\left[2\left(a+b-2c\right)E\left(\kappa ,p\right)-\left(b-c\right)F\left(\kappa ,p\right)\right]\hfill \\ +\frac{2}{3\left(a-c\right)\left(b-c\right)}\sqrt{\frac{\left(a-u\right)\left(u-b\right)}{{\left(u-c\right)}^3}}\hfill \end{array}$

  BY (235.20)

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

16. 

$\begin{array}{ll}{\displaystyle {\int }_u^a\frac{\text{d}x}{\sqrt{\left(a-x\right)\left(x-b\right){\left(x-c\right)}^5}}}\hfill & =\frac{2}{3{\left(b-c\right)}^2\sqrt{{\left(a-c\right)}^3}}\left[2\left(a+b-2c\right)E\left(\lambda ,p\right)-\left(b-c\right)F\left(\lambda ,p\right)\right]\hfill \\ -\frac{2[a}{}\hfill \end{array}$