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${\int }_{u}^{d}\sqrt{\frac{a-x}{{\left(b-x\right)}^{3}\left(c-x\right)\left(d-x\right)}}\text{d}x=\frac{2}{b-c}\sqrt{\frac{a-c}{b-d}}\left[F\left(\alpha ,q\right)-E\left(\alpha ,q\right)\right]+\frac{2}{b-d}\sqrt{\frac{\left(a-u\right)\left(d-u\right)}{\left(b-u\right)\left(c-u\right)}}$

BY (251.12)

$[a>b>c>d>u]$

50.

${\int }_{d}^{u}\sqrt{\frac{a-x}{{\left(b-x\right)}^{3}\left(c-x\right)\left(x-d\right)}}\text{d}x=\frac{2}{b-c}\sqrt{\frac{a-c}{b-d}}E\left(\beta ,r\right)-\frac{2\left(a-b\right)}{\left(b-c\right)\left(b-d\right)}\sqrt{\frac{\left(u-d\right)\left(c-u\right)}{\left(a-u\right)\left(b-u\right)}}$

BY (252.09)

$[a>b>c≥u>d]$

51.

${\int }_{u}^{c}\sqrt{\frac{a-x}{{\left(b-x\right)}^{3}\left(c-x\right)\left(x-d\right)}}\text{d}x=\frac{2}{b-c}\sqrt{\frac{a-c}{b-d}}E\left(\text{γ},r\right)$

BY (253.01)

$[a>b>c>u≥d]$

52.

${\int }_{c}^{u}\sqrt{\frac{a-x}{{\left(b-x\right)}^{3}\left(x-c\right)\left(x-d\right)}}\text{d}x=\frac{2}{b-c}\sqrt{\frac{a-c}{b-d}}\left[F\left(\text{δ},q\right)-E\left(\text{δ},q\right)\right]+\frac{2}{b-}$

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