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Statements
∫
y
x
a
α
+
b
α
t
a
δ
+
b
δ
t
d
t
s
(
t
)
=
2
3
d
α
β
d
α
γ
R
D
(
U
α
β
2
,
U
α
γ
2
,
U
α
δ
2
)
+
2
X
α
Y
α
X
δ
Y
δ
U
α
δ
,
superscript
subscript
𝑦
𝑥
subscript
𝑎
𝛼
subscript
𝑏
𝛼
𝑡
subscript
𝑎
𝛿
subscript
𝑏
𝛿
𝑡
𝑡
𝑠
𝑡
2
3
subscript
𝑑
𝛼
𝛽
subscript
𝑑
𝛼
𝛾
Carlson-integral-RD
superscript
subscript
𝑈
𝛼
𝛽
2
superscript
subscript
𝑈
𝛼
𝛾
2
superscript
subscript
𝑈
𝛼
𝛿
2
2
subscript
𝑋
𝛼
subscript
𝑌
𝛼
subscript
𝑋
𝛿
subscript
𝑌
𝛿
subscript
𝑈
𝛼
𝛿
{\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}},}}
U
α
δ
≠
0
subscript
𝑈
𝛼
𝛿
0
{\displaystyle{\displaystyle U_{\alpha\delta}\neq 0}}
R
D
(
x
,
y
,
z
)
Carlson-integral-RD
𝑥
𝑦
𝑧
{\displaystyle{\displaystyle R_{D}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
∫
{\displaystyle{\displaystyle\int}}
X
α
subscript
𝑋
𝛼
{\displaystyle{\displaystyle X_{\alpha}}}
U
n
subscript
𝑈
𝑛
{\displaystyle{\displaystyle U_{n}}}
Y
α
subscript
𝑌
𝛼
{\displaystyle{\displaystyle Y_{\alpha}}}
d
α
β
subscript
𝑑
𝛼
𝛽
{\displaystyle{\displaystyle d_{\alpha\beta}}}
s
(
t
)
𝑠
𝑡
{\displaystyle{\displaystyle s(t)}}
α
𝛼
{\displaystyle{\displaystyle\alpha}}
β
𝛽
{\displaystyle{\displaystyle\beta}}
γ
𝛾
{\displaystyle{\displaystyle\gamma}}
δ
𝛿
{\displaystyle{\displaystyle\delta}}
Identifiers
