Formula:7325

Digital Library of Mathematical Functions ID 19.29.E7

${\displaystyle{\displaystyle\int_{y}^{x}\frac{a_{\alpha}+b_{\alpha}t}{a_{\delta}+b_{\delta}t}\frac{\mathrm{d}t}{s(t)}=\tfrac{2}{3}d_{\alpha\beta}d_{\alpha\gamma}R_{D}\left(U_{\alpha\beta}^{2},U_{\alpha\gamma}^{2},U_{\alpha\delta}^{2}\right)+\frac{2X_{\alpha}Y_{\alpha}}{X_{\delta}Y_{\delta}U_{\alpha\delta}},}}$

Constraint(s)

${\displaystyle{\displaystyle U_{\alpha\delta}\neq 0}}$

Symbols List

• ${\displaystyle{\displaystyle R_{D}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}$: elliptic integral symmetric in only two variables
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle X_{\alpha}}}$: X α
• ${\displaystyle{\displaystyle U_{n}}}$: U n
• ${\displaystyle{\displaystyle Y_{\alpha}}}$: Y α
• ${\displaystyle{\displaystyle d_{\alpha\beta}}}$: d ⁢ α β
• ${\displaystyle{\displaystyle s(t)}}$: product
• ${\displaystyle{\displaystyle\alpha}}$: parameter
• ${\displaystyle{\displaystyle\beta}}$: parameter
• ${\displaystyle{\displaystyle\gamma}}$: parameter
• ${\displaystyle{\displaystyle\delta}}$: parameter
 

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