$\begin{array}{ll}{\int }_{u}^{c}\frac{\text{d}x}{\left(p-x\right)\sqrt{\left(a-x\right)\left(b-x\right)\left(c-x\right)\left(x-d\right)}}\hfill & =\frac{2}{\left(p-b\right)\left(p-c\right)\sqrt{\left(a-c\right)\left(b-d\right)}}\hfill \\ ×\left[\left(c-b\right)\prod \left(\text{γ},\frac{\left(c-d\right)\left(p-b\right)}{\left(b-d\right)\left(p-c\right)},r\right)+\left(p-c\right)F\left(\text{γ},r\right)\right]\hfill \end{array}$ BY (253.39) 4.

$\begin{array}{ll}{\int }_{c}^{u}\frac{\text{d}x}{\left(p-x\right)\sqrt{\left(a-x\right)\left(b-x\right)\left(x-c\right)\left(x-d\right)}}\hfill & =\frac{2}{\left(p-c\right)\left(p-d\right)\sqrt{\left(a-c\right)\left(b-d\right)}}\hfill \\ ×\left[\left(c-d\right)\prod \left(\text{δ},\frac{\left(b-c\right)\left(p-d\right)}{\left(b-d\right)\left(p-c\right)},q\right)+\left(p-c\right)F\left(\text{δ},q\right)\right]\hfill \end{array}$ BY (254.39) 5.

$\begin{array}{l}{\int }_{u}^{b}\frac{\text{d}x}{\left(p-x\right)\sqrt{\left(a-x\right)\left(b-x\right)\left(x-c\right)\left(x-d\right)}}\hfill \\ =\frac{2}{\left(p-a\right)\left(p-b\right)\sqrt{\left(a-c\right)\left(b-d\right)}}\hfill \\ ×\left[\left(b-a\right)\prod \left(\kappa ,\frac{\left(b-c\right)\left(p-a\right)}{}\hfill \end{array}$

Get Table of Integrals, Series, and Products, 8th Edition now with O’Reilly online learning.

O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers.