DLMF:19.29.E10 (Q6635)

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DLMF:19.29.E10
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    Statements

    test
    ∫ u b a - t ( b - t ) ⁢ ( t - c ) 3 ⁢ d t = - 2 3 ⁢ ( a - b ) ⁢ ( b - u ) 3 / 2 ⁢ R D ⁡ + 2 b - c ⁢ ( a - u ) ⁢ ( b - u ) u - c , superscript subscript 𝑢 𝑏 𝑎 𝑡 𝑏 𝑡 superscript 𝑡 𝑐 3 𝑡 2 3 𝑎 𝑏 superscript 𝑏 𝑢 3 2 Carlson-integral-RD 𝑎 𝑏 𝑢 𝑐 𝑏 𝑐 𝑎 𝑢 𝑎 𝑏 𝑏 𝑐 2 𝑏 𝑐 𝑎 𝑢 𝑏 𝑢 𝑢 𝑐 {\displaystyle{\displaystyle\int_{u}^{b}\sqrt{\frac{a-t}{(b-t)(t-c)^{3}}}% \mathrm{d}t=-\tfrac{2}{3}{(a-b)}{(b-u)}^{3/2}R_{D}+\frac{2}{b-c}\sqrt{\frac{(a% -u)(b-u)}{u-c}},}}
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    DLMF id
    DLMF:19.29.E10
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    constraint
    a > b > u > c 𝑎 𝑏 𝑢 𝑐 {\displaystyle{\displaystyle a>b>u>c}}
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