Series[Sin[Sqrt[(2+Cos[ϕ]Cos[θ])^2+(Cos[ϕ]Sin[θ])^2]]^2,{ϕ,0,14},{θ,0,14}]​​
2
Sin[3]
-
2
3
(Cos[3]Sin[3])
2
θ
+
⋯6⋯
+
15
O[θ]
+-Cos[3]Sin[3]+
1
9
(3
2
Cos[3]
+2Cos[3]Sin[3]-3
2
Sin[3]
)
2
θ
+
⋯6⋯
+
15
O[θ]
2
ϕ
+
⋯5⋯
+
-10334415
2
Cos[3]
-20840821Cos[3]Sin[3]+10334415
2
⋯1⋯
43589145600
+
(
⋯1⋯
)
2
θ
1176906931200
+(
⋯1⋯
)
4
θ
+
⋯3⋯
+
⋯1⋯
+(
⋯1⋯
)
14
θ
+
15
O[θ]
14
ϕ
+
15
O[ϕ]
large output
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​​Integrate
2
Sin[3]
-
2
3
(Cos[3]Sin[3])
2
θ
+
⋯6⋯
+
15
O[θ]
+-Cos[3]Sin[3]+
1
9
(3
2
Cos[3]
+2Cos[3]Sin[3]-3
2
Sin[3]
)
2
θ
+
⋯6⋯
+
15
O[θ]
2
ϕ
+
⋯5⋯
+
-10334415
2
Cos[3]
-20840821Cos[3]Sin[3]+10334415
2
⋯1⋯
43589145600
+
(
⋯1⋯
)
2
θ
1176906931200
+(
⋯1⋯
)
4
θ
+
⋯3⋯
+
⋯1⋯
+(
⋯1⋯
)
14
θ
+
15
O[θ]
14
ϕ
+
15
O[ϕ]
large output
show less
show more
show all
set size limit...
,{ϕ,0,Pi/2},{θ,0,Pi/2}​​​​​​
N(
2
π
(2258761631561109161698538815488000000
2
Sin[3]
+
28
π
(16328007195575912391Cos[6]-7543595689162512158Sin[6])-60480
24
π
(12470879528757201Cos[6]-354563179929057938Sin[6])+670924800
22
π
(684071798910657Cos[6]-372030643966288Sin[6])-33476463820800
18
π
(446421038181Cos[6]-6160245905554Sin[6])+669529276416000
16
π
(4770631444917Cos[6]-2009678425934Sin[6])-17354198844702720000
12
π
(11027593158Cos[6]-41854053445Sin[6])+25267713517887160320000
10
π
(385324062Cos[6]-72735673Sin[6])-259355897215919537415782400000
6
π
(2946Cos[6]-4679Sin[6])-156858446636188136229065195520000000
2
π
Sin[6]+43571790732274482285851443200000
4
π
(354Cos[6]+73Sin[6])-20012029106166630973440000
8
π
(3549894Cos[6]+5059067Sin[6])-48206107901952000
14
π
(840771833154Cos[6]+723869366249Sin[6])-271724544000
20
π
(34388822185617Cos[6]+21706295515630Sin[6])-5040
26
π
(122223438095857563Cos[6]+80406950294045818Sin[6])))9035046526244436646794155261952000000
1.02822