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Searched refs:Sin (Results 1 – 25 of 3194) sorted by relevance

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/dports/games/spacejunk/spacejunk-1.0.5/data/art/
H A D	titlescreen.gpl	`5 0 0 0 Sin nombre 6 255 255 255 Sin nombre 7 70 70 70 Sin nombre 8 66 51 52 Sin nombre 9 252 243 244 Sin nombre 10 245 236 237 Sin nombre 11 102 69 78 Sin nombre 12 90 23 42 Sin nombre 13 224 30 93 Sin nombre 14 59 10 25 Sin nombre [all …]`
H A D	spacejunk.gpl	`5 0 0 0 Sin nombre 6 255 255 255 Sin nombre 7 255 0 255 Sin nombre 8 216 47 61 Sin nombre 9 56 8 24 Sin nombre 10 72 24 40 Sin nombre 11 136 88 104 Sin nombre 12 40 8 24 Sin nombre 13 76 56 72 Sin nombre 14 91 72 88 Sin nombre [all …]`
/dports/math/reduce/Reduce-svn5758-src/contrib/rubi-red/rubi4/Rubi-Red/
H A D	sin(x)^m (a+a sin(x))^n.m	5 (Sin[c+d x]^m (A+B Sin[c+d x]+C Sin[c+d x]^2) (a+b Sin[c+d x])^n when a^2=b^2) 9 (Sin[c+d x]^m (a+a Sin[c+d x])^n) 16 {Sin[x]^4/(a + aSin[x]), x, 5, -((3x)/(2a)) - (4Cos[x])/a + (4Cos[x]^3)/(3a) + (3Cos[x]Sin[… 17 {Sin[x]^3/(a + aSin[x]), x, 4, (3x)/(2a) + (2Cos[x])/a - (3Cos[x]Sin[x])/(2a) + (Cos[x]Sin[… 19 {Sin[x]^1/(a + aSin[x]), x, 2, x/a + Cos[x]/(a + aSin[x])} 26 …Sin[x]^4/(a + aSin[x])^2, x, 5, (7x)/(2a^2) + (16Cos[x])/(3a^2) - (7Cos[x]Sin[x])/(2a^2) +… 37 …Sin[x]^5/(a + aSin[x])^3, x, 6, (13x)/(2a^3) + (152Cos[x])/(15a^3) - (13Cos[x]Sin[x])/(2a^… 38 …Sin[x]^4/(a + aSin[x])^3, x, 5, -((3x)/a^3) - (9Cos[x])/(5a^3) + (Cos[x]Sin[x]^3)/(5(a + aS… 98 (Sin[c+d x]^m (A+B Sin[c+d x]) (a+a Sin[c+d x])^n) 136 (Sin[c+d x]^m (A+C Sin[c+d x]^2) (a+a Sin[c+d x])^n*) [all …]
H A D	sin(x)^m (a+b sin(x))^n.m	5 (Sin[c+d x]^m (A+B Sin[c+d x]+C Sin[c+d x]^2) (a+b Sin[c+d x])^n) 9 (Sin[c+d x]^m (a+b Sin[c+d x])^n) 98 (Sin[c+d x]^m (A+B Sin[c+d x]) (a+b Sin[c+d x])^n) 102 (Integrands of the form Sin[c+d x]^m (A+B Sin[c+d x]) (a+b Sin[c+d x])^n) 114 {(a + bSin[x])/(b + aSin[x])^2, x, 2, -(Cos[x]/(b + aSin[x]))} 132 (Sin[c+d x]^m (A+C Sin[c+d x]^2) (a+b Sin[c+d x])^n) 136 (Integrands of the form Sin[c+d x]^m (A+C Sin[c+d x]^2) (a+b Sin[c+d x])^n) 144 (Sin[c+d x]^m (A+B Sin[c+d x]+C Sin[c+d x]^2) (a+b Sin[c+d x])^n) 148 (Integrands of the form Sin[c+d x]^m (A+B Sin[c+d x]+C Sin[c+d x]^2) (a+b Sin[c+d x])^n) 155 (Integrands of the form Sin[c+d x]^m (A+B Sin[c+d x]+C Sin[c+d x]^2) (a+b Sin[c+d x])^(n/2)*) [all …]
/dports/math/reduce/Reduce-svn5758-src/contrib/rubi-red/
H A D	sin(x)^m (a+a sin(x))^n.m	5 (Sin[c+d x]^m (A+B Sin[c+d x]+C Sin[c+d x]^2) (a+b Sin[c+d x])^n when a^2=b^2) 9 (Sin[c+d x]^m (a+a Sin[c+d x])^n) 16 {Sin[x]^4/(a + aSin[x]), x, 5, -((3x)/(2a)) - (4Cos[x])/a + (4Cos[x]^3)/(3a) + (3Cos[x]Sin[… 17 {Sin[x]^3/(a + aSin[x]), x, 4, (3x)/(2a) + (2Cos[x])/a - (3Cos[x]Sin[x])/(2a) + (Cos[x]Sin[… 19 {Sin[x]^1/(a + aSin[x]), x, 2, x/a + Cos[x]/(a + aSin[x])} 26 …Sin[x]^4/(a + aSin[x])^2, x, 5, (7x)/(2a^2) + (16Cos[x])/(3a^2) - (7Cos[x]Sin[x])/(2a^2) +… 37 …Sin[x]^5/(a + aSin[x])^3, x, 6, (13x)/(2a^3) + (152Cos[x])/(15a^3) - (13Cos[x]Sin[x])/(2a^… 38 …Sin[x]^4/(a + aSin[x])^3, x, 5, -((3x)/a^3) - (9Cos[x])/(5a^3) + (Cos[x]Sin[x]^3)/(5(a + aS… 98 (Sin[c+d x]^m (A+B Sin[c+d x]) (a+a Sin[c+d x])^n) 136 (Sin[c+d x]^m (A+C Sin[c+d x]^2) (a+a Sin[c+d x])^n*) [all …]
H A D	sin(x)^m (a+b sin(x))^n.m	5 (Sin[c+d x]^m (A+B Sin[c+d x]+C Sin[c+d x]^2) (a+b Sin[c+d x])^n) 9 (Sin[c+d x]^m (a+b Sin[c+d x])^n) 98 (Sin[c+d x]^m (A+B Sin[c+d x]) (a+b Sin[c+d x])^n) 102 (Integrands of the form Sin[c+d x]^m (A+B Sin[c+d x]) (a+b Sin[c+d x])^n) 114 {(a + bSin[x])/(b + aSin[x])^2, x, 2, -(Cos[x]/(b + aSin[x]))} 132 (Sin[c+d x]^m (A+C Sin[c+d x]^2) (a+b Sin[c+d x])^n) 136 (Integrands of the form Sin[c+d x]^m (A+C Sin[c+d x]^2) (a+b Sin[c+d x])^n) 144 (Sin[c+d x]^m (A+B Sin[c+d x]+C Sin[c+d x]^2) (a+b Sin[c+d x])^n) 148 (Integrands of the form Sin[c+d x]^m (A+B Sin[c+d x]+C Sin[c+d x]^2) (a+b Sin[c+d x])^n) 155 (Integrands of the form Sin[c+d x]^m (A+B Sin[c+d x]+C Sin[c+d x]^2) (a+b Sin[c+d x])^(n/2)*) [all …]
/dports/math/reduce/Reduce-svn5758-src/packages/rubi_red/tests/TrigFunctions/
H A D	sin(x)^m (a+a sin(x))^n.m	5 (Sin[c+d x]^m (A+B Sin[c+d x]+C Sin[c+d x]^2) (a+b Sin[c+d x])^n when a^2=b^2) 9 (Sin[c+d x]^m (a+a Sin[c+d x])^n) 16 {Sin[x]^4/(a + aSin[x]), x, 4, -((3x)/(2a)) - (8Cos[x])/(3a) + (3Cos[x]Sin[x])/(2a) - (4Co… 17 {Sin[x]^3/(a + aSin[x]), x, 3, (3x)/(2a) + (2Cos[x])/a - (3Cos[x]Sin[x])/(2a) + (Cos[x]Sin[… 19 {Sin[x]^1/(a + aSin[x]), x, 2, x/a + Cos[x]/(a + aSin[x])} 26 …Sin[x]^4/(a + aSin[x])^2, x, 4, (7x)/(2a^2) + (16Cos[x])/(3a^2) - (7Cos[x]Sin[x])/(2a^2) +… 29 {Sin[x]^1/(a + aSin[x])^2, x, 2, Cos[x]/(3(a + aSin[x])^2) - (2Cos[x])/(3a(a + aSin[x]))} 37 …Sin[x]^3/(a + aSin[x])^3, x, 4, x/a^3 + (Cos[x]Sin[x]^2)/(5(a + aSin[x])^3) + (7Cos[x]Sin[x]… 100 (Sin[c+d x]^m (A+B Sin[c+d x]) (a+a Sin[c+d x])^n) 138 (Sin[c+d x]^m (A+C Sin[c+d x]^2) (a+a Sin[c+d x])^n) [all …]
H A D	sin(x)^m (a+b sin(x))^n.m	5 (Sin[c+d x]^m (A+B Sin[c+d x]+C Sin[c+d x]^2) (a+b Sin[c+d x])^n) 9 (Sin[c+d x]^m (a+b Sin[c+d x])^n) 13 (Integrands of the form Sin[c+d x]^m (a+b Sin[c+d x])^n) 86 (Sin[c+d x]^m (A+B Sin[c+d x]) (a+b Sin[c+d x])^n) 90 (Integrands of the form Sin[c+d x]^m (A+B Sin[c+d x]) (a+b Sin[c+d x])^n) 102 {(a + bSin[x])/(b + aSin[x])^2, x, 2, -(Cos[x]/(b + aSin[x]))} 120 (Sin[c+d x]^m (A+C Sin[c+d x]^2) (a+b Sin[c+d x])^n) 124 (Integrands of the form Sin[c+d x]^m (A+C Sin[c+d x]^2) (a+b Sin[c+d x])^n) 132 (Sin[c+d x]^m (A+B Sin[c+d x]+C Sin[c+d x]^2) (a+b Sin[c+d x])^n) 136 (Integrands of the form Sin[c+d x]^m (A+B Sin[c+d x]+C Sin[c+d x]^2) (a+b Sin[c+d x])^n*) [all …]
H A D	SineFunctions.m	44 {Sin[x]^(3/2)/x^3, x, 1, (3/8)Int[1/(xSqrt[Sin[x]]), x] - (9/8)Int[Sin[x]^(3/2)/x, x] - (3Cos[x… 55 {1/(aSin[x]^2)^(1/2), x, 2, -((ArcTanh[Cos[x]]Sin[x])/Sqrt[aSin[x]^2])} 61 …Sin[x]^3)^(5/2),x, 6, -((2a^2Sqrt[aSin[x]^3](195EllipticF[Pi/4 - x/2, 2] + 195Cos[x]Sqrt[Si… 70 …Sin[x]^4)^(5/2),x, 6, (-(63/256))a^2Cot[x]Sqrt[aSin[x]^4] + (63/256)a^2xCsc[x]^2Sqrt[aSin… 71 …Sin[x]^4)^(3/2),x, 4, (-(5/16))aCot[x]Sqrt[aSin[x]^4] + (5/16)axCsc[x]^2Sqrt[aSin[x]^4] -… 73 {1/(aSin[x]^4)^(1/2), x, 2, -((Cos[x]Sin[x])/Sqrt[aSin[x]^4])} 209 {xSqrt[Sin[x]^2], x, 3, Sqrt[Sin[x]^2] - xCot[x]Sqrt[Sin[x]^2]} 420 {x/Sin[x]^(3/2) + xSqrt[Sin[x]], x, 2, -((2xCos[x])/Sqrt[Sin[x]]) + 4Sqrt[Sin[x]]} 422 {x/Sin[x]^(7/2) + (3/5)xSqrt[Sin[x]], x, 3, -((2xCos[x])/(5Sin[x]^(5/2))) - 4/(15Sin[x]^(3/2)… 482 {Cos[x]^3/(a + aSin[x]), x, 2, Sin[x]/a - Sin[x]^2/(2a)} [all …]
H A D	TrigFunctions.m	15 {Sin[x](Cos[x] + Sin[x]), x, 5, x/2 - (1/2)Cos[x]Sin[x] + Sin[x]^2/2} 54 {Sin[x]/(Sec[x] + Tan[x]), x, 5, -Log[1 + Sin[x]] + Sin[x]} 61 {Sin[x]/(Sec[x] - Tan[x]), x, 5, -Log[1 - Sin[x]] - Sin[x]} 393 {Cos[x]/Sqrt[2Sin[x] + Sin[x]^2], x, 2, 2ArcTanh[Sin[x]/Sqrt[2Sin[x] + Sin[x]^2]]} 493 {Cos[x]Cos[Sin[x]], x, 2, Sin[Sin[x]]} 494 {Cos[x]Cos[Sin[x]]Cos[Sin[Sin[x]]], x, 3, Sin[Sin[Sin[x]]]} 495 {Cos[x]Sec[Sin[x]], x, 2, ArcTanh[Sin[Sin[x]]]} 603 {(Cos[x](-3 + 2Sin[x]))/(2 - 3Sin[x] + Sin[x]^2), x, 2, Log[2 - 3Sin[x] + Sin[x]^2]} 610 {(Cos[x]Sin[x])/Sqrt[1 + Sin[x]], x, 3, (-(4/3))Sqrt[1 + Sin[x]] + (2/3)Sin[x]Sqrt[1 + Sin[x]]} 700 {Cos[x]Sin[2x]Sin[3x], x, 11, x/4 + (1/8)Sin[2x] - (1/16)Sin[4x] - (1/24)Sin[6x]} [all …]
/dports/math/reduce/Reduce-svn5758-src/contrib/rubi-red/mathematicatests/
H A D	sin(x)^m (a+a sin(x))^n.m	5 (Sin[c+d x]^m (A+B Sin[c+d x]+C Sin[c+d x]^2) (a+b Sin[c+d x])^n when a^2=b^2) 9 (Sin[c+d x]^m (a+a Sin[c+d x])^n) 16 {Sin[x]^4/(a + aSin[x]), x, 4, -((3x)/(2a)) - (8Cos[x])/(3a) + (3Cos[x]Sin[x])/(2a) - (4Co… 17 {Sin[x]^3/(a + aSin[x]), x, 3, (3x)/(2a) + (2Cos[x])/a - (3Cos[x]Sin[x])/(2a) + (Cos[x]Sin[… 19 {Sin[x]^1/(a + aSin[x]), x, 2, x/a + Cos[x]/(a + aSin[x])} 26 …Sin[x]^4/(a + aSin[x])^2, x, 4, (7x)/(2a^2) + (16Cos[x])/(3a^2) - (7Cos[x]Sin[x])/(2a^2) +… 29 {Sin[x]^1/(a + aSin[x])^2, x, 2, Cos[x]/(3(a + aSin[x])^2) - (2Cos[x])/(3a(a + aSin[x]))} 37 …Sin[x]^3/(a + aSin[x])^3, x, 4, x/a^3 + (Cos[x]Sin[x]^2)/(5(a + aSin[x])^3) + (7Cos[x]Sin[x]… 100 (Sin[c+d x]^m (A+B Sin[c+d x]) (a+a Sin[c+d x])^n) 138 (Sin[c+d x]^m (A+C Sin[c+d x]^2) (a+a Sin[c+d x])^n) [all …]
H A D	sin(x)^m (a+b sin(x))^n.m	5 (Sin[c+d x]^m (A+B Sin[c+d x]+C Sin[c+d x]^2) (a+b Sin[c+d x])^n) 9 (Sin[c+d x]^m (a+b Sin[c+d x])^n) 13 (Integrands of the form Sin[c+d x]^m (a+b Sin[c+d x])^n) 86 (Sin[c+d x]^m (A+B Sin[c+d x]) (a+b Sin[c+d x])^n) 90 (Integrands of the form Sin[c+d x]^m (A+B Sin[c+d x]) (a+b Sin[c+d x])^n) 102 {(a + bSin[x])/(b + aSin[x])^2, x, 2, -(Cos[x]/(b + aSin[x]))} 120 (Sin[c+d x]^m (A+C Sin[c+d x]^2) (a+b Sin[c+d x])^n) 124 (Integrands of the form Sin[c+d x]^m (A+C Sin[c+d x]^2) (a+b Sin[c+d x])^n) 132 (Sin[c+d x]^m (A+B Sin[c+d x]+C Sin[c+d x]^2) (a+b Sin[c+d x])^n) 136 (Integrands of the form Sin[c+d x]^m (A+B Sin[c+d x]+C Sin[c+d x]^2) (a+b Sin[c+d x])^n*) [all …]
H A D	SineFunctions.m	44 {Sin[x]^(3/2)/x^3, x, 1, (3/8)Int[1/(xSqrt[Sin[x]]), x] - (9/8)Int[Sin[x]^(3/2)/x, x] - (3Cos[x… 55 {1/(aSin[x]^2)^(1/2), x, 2, -((ArcTanh[Cos[x]]Sin[x])/Sqrt[aSin[x]^2])} 61 …Sin[x]^3)^(5/2),x, 6, -((2a^2Sqrt[aSin[x]^3](195EllipticF[Pi/4 - x/2, 2] + 195Cos[x]Sqrt[Si… 70 …Sin[x]^4)^(5/2),x, 6, (-(63/256))a^2Cot[x]Sqrt[aSin[x]^4] + (63/256)a^2xCsc[x]^2Sqrt[aSin… 71 …Sin[x]^4)^(3/2),x, 4, (-(5/16))aCot[x]Sqrt[aSin[x]^4] + (5/16)axCsc[x]^2Sqrt[aSin[x]^4] -… 73 {1/(aSin[x]^4)^(1/2), x, 2, -((Cos[x]Sin[x])/Sqrt[aSin[x]^4])} 209 {xSqrt[Sin[x]^2], x, 3, Sqrt[Sin[x]^2] - xCot[x]Sqrt[Sin[x]^2]} 420 {x/Sin[x]^(3/2) + xSqrt[Sin[x]], x, 2, -((2xCos[x])/Sqrt[Sin[x]]) + 4Sqrt[Sin[x]]} 422 {x/Sin[x]^(7/2) + (3/5)xSqrt[Sin[x]], x, 3, -((2xCos[x])/(5Sin[x]^(5/2))) - 4/(15Sin[x]^(3/2)… 482 {Cos[x]^3/(a + aSin[x]), x, 2, Sin[x]/a - Sin[x]^2/(2a)} [all …]
H A D	TrigFunctions.m	15 {Sin[x](Cos[x] + Sin[x]), x, 5, x/2 - (1/2)Cos[x]Sin[x] + Sin[x]^2/2} 54 {Sin[x]/(Sec[x] + Tan[x]), x, 5, -Log[1 + Sin[x]] + Sin[x]} 61 {Sin[x]/(Sec[x] - Tan[x]), x, 5, -Log[1 - Sin[x]] - Sin[x]} 393 {Cos[x]/Sqrt[2Sin[x] + Sin[x]^2], x, 2, 2ArcTanh[Sin[x]/Sqrt[2Sin[x] + Sin[x]^2]]} 493 {Cos[x]Cos[Sin[x]], x, 2, Sin[Sin[x]]} 494 {Cos[x]Cos[Sin[x]]Cos[Sin[Sin[x]]], x, 3, Sin[Sin[Sin[x]]]} 495 {Cos[x]Sec[Sin[x]], x, 2, ArcTanh[Sin[Sin[x]]]} 603 {(Cos[x](-3 + 2Sin[x]))/(2 - 3Sin[x] + Sin[x]^2), x, 2, Log[2 - 3Sin[x] + Sin[x]^2]} 610 {(Cos[x]Sin[x])/Sqrt[1 + Sin[x]], x, 3, (-(4/3))Sqrt[1 + Sin[x]] + (2/3)Sin[x]Sqrt[1 + Sin[x]]} 700 {Cos[x]Sin[2x]Sin[3x], x, 11, x/4 + (1/8)Sin[2x] - (1/16)Sin[4x] - (1/24)Sin[6x]} [all …]
/dports/math/reduce/Reduce-svn5758-src/contrib/rubi-red/rubi4/IntegrationProblems/MathematicaSyntaxFiles/TrigFunctions/
H A D	sin(x)^m (a+a sin(x))^n.m	5 (Sin[c+d x]^m (A+B Sin[c+d x]+C Sin[c+d x]^2) (a+b Sin[c+d x])^n when a^2=b^2) 9 (Sin[c+d x]^m (a+a Sin[c+d x])^n) 16 {Sin[x]^4/(a + aSin[x]), x, 4, -((3x)/(2a)) - (8Cos[x])/(3a) + (3Cos[x]Sin[x])/(2a) - (4Co… 17 {Sin[x]^3/(a + aSin[x]), x, 3, (3x)/(2a) + (2Cos[x])/a - (3Cos[x]Sin[x])/(2a) + (Cos[x]Sin[… 19 {Sin[x]^1/(a + aSin[x]), x, 2, x/a + Cos[x]/(a + aSin[x])} 26 …Sin[x]^4/(a + aSin[x])^2, x, 4, (7x)/(2a^2) + (16Cos[x])/(3a^2) - (7Cos[x]Sin[x])/(2a^2) +… 29 {Sin[x]^1/(a + aSin[x])^2, x, 2, Cos[x]/(3(a + aSin[x])^2) - (2Cos[x])/(3a(a + aSin[x]))} 37 …Sin[x]^3/(a + aSin[x])^3, x, 4, x/a^3 + (Cos[x]Sin[x]^2)/(5(a + aSin[x])^3) + (7Cos[x]Sin[x]… 100 (Sin[c+d x]^m (A+B Sin[c+d x]) (a+a Sin[c+d x])^n) 138 (Sin[c+d x]^m (A+C Sin[c+d x]^2) (a+a Sin[c+d x])^n) [all …]
H A D	sin(x)^m (a+b sin(x))^n.m	5 (Sin[c+d x]^m (A+B Sin[c+d x]+C Sin[c+d x]^2) (a+b Sin[c+d x])^n) 9 (Sin[c+d x]^m (a+b Sin[c+d x])^n) 13 (Integrands of the form Sin[c+d x]^m (a+b Sin[c+d x])^n) 86 (Sin[c+d x]^m (A+B Sin[c+d x]) (a+b Sin[c+d x])^n) 90 (Integrands of the form Sin[c+d x]^m (A+B Sin[c+d x]) (a+b Sin[c+d x])^n) 102 {(a + bSin[x])/(b + aSin[x])^2, x, 2, -(Cos[x]/(b + aSin[x]))} 120 (Sin[c+d x]^m (A+C Sin[c+d x]^2) (a+b Sin[c+d x])^n) 124 (Integrands of the form Sin[c+d x]^m (A+C Sin[c+d x]^2) (a+b Sin[c+d x])^n) 132 (Sin[c+d x]^m (A+B Sin[c+d x]+C Sin[c+d x]^2) (a+b Sin[c+d x])^n) 136 (Integrands of the form Sin[c+d x]^m (A+B Sin[c+d x]+C Sin[c+d x]^2) (a+b Sin[c+d x])^n*) [all …]
H A D	SineFunctions.m	44 {Sin[x]^(3/2)/x^3, x, 1, (3/8)Int[1/(xSqrt[Sin[x]]), x] - (9/8)Int[Sin[x]^(3/2)/x, x] - (3Cos[x… 55 {1/(aSin[x]^2)^(1/2), x, 2, -((ArcTanh[Cos[x]]Sin[x])/Sqrt[aSin[x]^2])} 61 …Sin[x]^3)^(5/2),x, 6, -((2a^2Sqrt[aSin[x]^3](195EllipticF[Pi/4 - x/2, 2] + 195Cos[x]Sqrt[Si… 70 …Sin[x]^4)^(5/2),x, 6, (-(63/256))a^2Cot[x]Sqrt[aSin[x]^4] + (63/256)a^2xCsc[x]^2Sqrt[aSin… 71 …Sin[x]^4)^(3/2),x, 4, (-(5/16))aCot[x]Sqrt[aSin[x]^4] + (5/16)axCsc[x]^2Sqrt[aSin[x]^4] -… 73 {1/(aSin[x]^4)^(1/2), x, 2, -((Cos[x]Sin[x])/Sqrt[aSin[x]^4])} 209 {xSqrt[Sin[x]^2], x, 3, Sqrt[Sin[x]^2] - xCot[x]Sqrt[Sin[x]^2]} 420 {x/Sin[x]^(3/2) + xSqrt[Sin[x]], x, 2, -((2xCos[x])/Sqrt[Sin[x]]) + 4Sqrt[Sin[x]]} 422 {x/Sin[x]^(7/2) + (3/5)xSqrt[Sin[x]], x, 3, -((2xCos[x])/(5Sin[x]^(5/2))) - 4/(15Sin[x]^(3/2)… 482 {Cos[x]^3/(a + aSin[x]), x, 2, Sin[x]/a - Sin[x]^2/(2a)} [all …]
H A D	TrigFunctions.m	15 {Sin[x](Cos[x] + Sin[x]), x, 5, x/2 - (1/2)Cos[x]Sin[x] + Sin[x]^2/2} 54 {Sin[x]/(Sec[x] + Tan[x]), x, 5, -Log[1 + Sin[x]] + Sin[x]} 61 {Sin[x]/(Sec[x] - Tan[x]), x, 5, -Log[1 - Sin[x]] - Sin[x]} 393 {Cos[x]/Sqrt[2Sin[x] + Sin[x]^2], x, 2, 2ArcTanh[Sin[x]/Sqrt[2Sin[x] + Sin[x]^2]]} 493 {Cos[x]Cos[Sin[x]], x, 2, Sin[Sin[x]]} 494 {Cos[x]Cos[Sin[x]]Cos[Sin[Sin[x]]], x, 3, Sin[Sin[Sin[x]]]} 495 {Cos[x]Sec[Sin[x]], x, 2, ArcTanh[Sin[Sin[x]]]} 603 {(Cos[x](-3 + 2Sin[x]))/(2 - 3Sin[x] + Sin[x]^2), x, 2, Log[2 - 3Sin[x] + Sin[x]^2]} 610 {(Cos[x]Sin[x])/Sqrt[1 + Sin[x]], x, 3, (-(4/3))Sqrt[1 + Sin[x]] + (2/3)Sin[x]Sqrt[1 + Sin[x]]} 700 {Cos[x]Sin[2x]Sin[3x], x, 11, x/4 + (1/8)Sin[2x] - (1/16)Sin[4x] - (1/24)Sin[6x]} [all …]
/dports/math/reduce/Reduce-svn5758-src/packages/rubi_red/tests4/TrigFunctions/
H A D	7.1.1 sin(c+d x)^m (a+a sin(c+d x))^n.m	5 (Sin[c+d x]^m (A+B Sin[c+d x]+C Sin[c+d x]^2) (a+b Sin[c+d x])^n when a^2=b^2) 9 (Sin[c+d x]^m (a+a Sin[c+d x])^n) 16 {Sin[x]^4/(a + aSin[x]), x, 4, -((3x)/(2a)) - (4Cos[x])/a + (4Cos[x]^3)/(3a) + (3Cos[x]Sin[… 17 {Sin[x]^3/(a + aSin[x]), x, 3, (3x)/(2a) + (2Cos[x])/a - (3Cos[x]Sin[x])/(2a) + (Cos[x]Sin[… 19 {Sin[x]^1/(a + aSin[x]), x, 2, x/a + Cos[x]/(a + aSin[x])} 26 …Sin[x]^4/(a + aSin[x])^2, x, 5, (7x)/(2a^2) + (16Cos[x])/(3a^2) - (7Cos[x]Sin[x])/(2a^2) +… 37 …Sin[x]^5/(a + aSin[x])^3, x, 6, (13x)/(2a^3) + (152Cos[x])/(15a^3) - (13Cos[x]Sin[x])/(2a^… 38 …Sin[x]^4/(a + aSin[x])^3, x, 5, -((3x)/a^3) - (9Cos[x])/(5a^3) + (Cos[x]Sin[x]^3)/(5(a + aS… 98 (Sin[c+d x]^m (A+B Sin[c+d x]) (a+a Sin[c+d x])^n) 140 (Sin[c+d x]^m (A+C Sin[c+d x]^2) (a+a Sin[c+d x])^n*) [all …]
H A D	7.1.2 sin(c+d x)^m (a+b sin(c+d x))^n.m	5 (Sin[c+d x]^m (A+B Sin[c+d x]+C Sin[c+d x]^2) (a+b Sin[c+d x])^n) 9 (Sin[c+d x]^m (a+b Sin[c+d x])^n) 13 (Integrands of the form Sin[c+d x]^m (a+b Sin[c+d x])^n) 111 (Sin[c+d x]^m (A+B Sin[c+d x]) (a+b Sin[c+d x])^n) 115 (Integrands of the form Sin[c+d x]^m (A+B Sin[c+d x]) (a+b Sin[c+d x])^n) 127 {(a + bSin[x])/(b + aSin[x])^2, x, 2, -(Cos[x]/(b + aSin[x]))} 145 (Sin[c+d x]^m (A+C Sin[c+d x]^2) (a+b Sin[c+d x])^n) 157 (Sin[c+d x]^m (A+B Sin[c+d x]+C Sin[c+d x]^2) (a+b Sin[c+d x])^n) 161 (Integrands of the form Sin[c+d x]^m (A+B Sin[c+d x]+C Sin[c+d x]^2) (a+b Sin[c+d x])^n) 168 (Integrands of the form Sin[c+d x]^m (A+B Sin[c+d x]+C Sin[c+d x]^2) (a+b Sin[c+d x])^(n/2)*) [all …]
H A D	7.1.3 trig(c+d x)^m (a+b sin(c+d x))^n.m	78 {Cos[x]^5/(a + aSin[x]), x, 4, Cos[x]^4/(4a) + Sin[x]/a - Sin[x]^3/(3a), Sin[x]/a - Sin[x]^2/(2… 80 {Cos[x]^3/(a + aSin[x]), x, 3, Sin[x]/a - Sin[x]^2/(2a)} 86 {Sec[x]^3/(a + aSin[x]), x, 5, (3ArcTanh[Sin[x]])/(8a) + 1/(8a(1 - Sin[x])) - 1/(8a(1 + Sin[… 92 {Cos[x]^7/(a + aSin[x])^2, x, 4, Sin[x]/a^2 - Sin[x]^2/a^2 + Sin[x]^4/(2a^2) - Sin[x]^5/(5a^2)} 96 {Cos[x]^3/(a + aSin[x])^2, x, 4, (2Log[1 + Sin[x]])/a^2 - Sin[x]/a^2} 102 … + aSin[x])^2, x, 5, ArcTanh[Sin[x]]/(4a^2) + 1/(16a^2(1 - Sin[x])) - 1/(12a^2(1 + Sin[x])^3… 111 {Cos[x]^3/(1 + Sin[x])^3, x, 4, -Log[1 + Sin[x]] - 2/(1 + Sin[x])} 112 {Cos[x]^3/(1 - Sin[x])^3, x, 4, Log[1 - Sin[x]] + 2/(1 - Sin[x])} 482 …Sin[x]), x, 5, (5ArcTanh[Sin[x]])/(16a) + 1/(32a(1 - Sin[x])^2) - 3/(16a(1 - Sin[x])) + 1/(2… 503 {Cot[x]^1/(a + aSin[x])^2, x, 3, Log[Sin[x]]/a^2 - Log[1 + Sin[x]]/a^2 + 1/(a^2(1 + Sin[x]))} [all …]
H A D	3.2 trig(a+b x)^m trig(c+d x)^n.m	12 (Integrands of the form Sin[a+b x]^m Sin[c+d x]^n) 15 {Sin[a + bx]Sin[c + dx]^n, x, 0, Int[Sin[a + bx]Sin[c + dx]^n, x]} 17 …Sin[a + bx]Sin[c + dx]^3, x, 6, -(Sin[a - 3c + (b - 3d)x]/(8(b - 3d))) + (3Sin[a - c + (b… 19 {Sin[a + bx]Sin[c + dx]^1, x, 4, Sin[a - c + (b - d)x]/(2(b - d)) - Sin[a + c + (b + d)x]/(2… 20 {Sin[a + bx]Csc[c + bx]^1, x, 3, xCos[a - c] + (Log[Sin[c + bx]]Sin[a - c])/b} 28 {Sin[a + bx]^2Sin[c + dx]^n, x, 0, Int[Sin[a + bx]^2Sin[c + dx]^n, x]} 31 {Sin[a + bx]^2Sin[c + dx]^2, x, 6, x/4 - Sin[2a + 2bx]/(8b) + Sin[2(a - c) + 2(b - d)x]/(… 35 {Sin[a + bx]^3Sin[c + dx]^n, x, 0, Int[Sin[a + bx]^3Sin[c + dx]^n, x]} 37 …Sin[a + bx]^3Sin[c + dx]^1, x, 6, (3Sin[a - c + (b - d)x])/(8(b - d)) - Sin[3a - c + (3b -… 73 {Cos[a + bx]/Sin[c + bx]^1, x, 3, (Cos[a - c]Log[Sin[c + bx]])/b - x*Sin[a - c]} [all …]
H A D	TrigFunctions.m	421 {Sin[2x]Sin[x],x, 2, (2Sin[x]^3)/3} 422 {Sin[3x]Sin[x],x, 3, (1/4)Sin[2x] - (1/8)Sin[4x]} 423 {Sin[4x]Sin[x],x, 3, (1/6)Sin[3x] - (1/10)Sin[5x]} 1296 {Cos[x]/Sqrt[2Sin[x] + Sin[x]^2], x, 2, 2ArcTanh[Sin[x]/Sqrt[2Sin[x] + Sin[x]^2]]} 1391 {Cos[x]Cos[Sin[x]], x, 2, Sin[Sin[x]]} 1392 {Cos[x]Cos[Sin[x]]Cos[Sin[Sin[x]]], x, 3, Sin[Sin[Sin[x]]]} 1501 {(Cos[x](-3 + 2Sin[x]))/(2 - 3Sin[x] + Sin[x]^2), x, 2, Log[2 - 3Sin[x] + Sin[x]^2]} 1503 {Cos[x]/(Sin[x] + Sin[x]^2), x, 3, Log[Sin[x]] - Log[1 + Sin[x]]} 1596 {Sin[x]Sin[2x]Sin[3x], x, 3, (3Sin[x]^4)/2 - (4Sin[x]^6)/3} 1598 {Cos[x]Sin[2x]Sin[3x], x, 11, x/4 + (1/8)Sin[2x] - (1/16)Sin[4x] - (1/24)Sin[6*x]} [all …]
/dports/math/reduce/Reduce-svn5758-src/packages/rubi_red/rubi-rules/TrigFunctions/
H A D	RecurrenceEquations.m	13 (2b(n+1)(a^2-b^2)\[Integral](Sin[z]^j)^m (A+B Sin[z]^k+C Sin[z]^(2k)) (a+b Sin[z]^k)^n \[Different… 28 (b(2j k m+2n+k+3)\[Integral](Sin[z]^j)^m (A+B Sin[z]^k+C Sin[z]^(2k)) (a+b Sin[z]^k)^n \[Different… 29 (-2C Cos[z](Sin[z]^j)^m (a+b Sin[z]^k)^(n+1)+) 43 ((2j k m+2n+k+3)\[Integral](Sin[z]^j)^m (A+B Sin[z]^k+C Sin[z]^(2k)) (a+b Sin[z]^k)^n \[Differenti… 44 (-2C Cos[z](Sin[z]^j)^(m+j k) (a+b Sin[z]^k)^n+) 58 ((2j k m+k+1)\[Integral](Sin[z]^j)^m (A+B Sin[z]^k+C Sin[z]^(2k)) (a+b Sin[z]^k)^n \[DifferentialD… 59 (2A Cos[z](Sin[z]^j)^(m+j k) (a+b Sin[z]^k)^n+) 73 (a(2j k m+k+1)\[Integral](Sin[z]^j)^m (A+B Sin[z]^k+C Sin[z]^(2k)) (a+b Sin[z]^k)^n \[Differential… 88 (2a(n+1) (a^2-b^2)\[Integral](Sin[z]^j)^m (A+B Sin[z]^k+C Sin[z]^(2k)) (a+b Sin[z]^k)^n \[Differen… 108 (2a^2 (2n+1)\[Integral](Sin[z]^j)^m (A+B Sin[z]^k) (a+b Sin[z]^k)^n \[DifferentialD]z=) [all …]
/dports/math/py-mathics/Mathics3-2.2.0/mathics/packages/analytica/
H A D	trigonometric.m	20 simplifications to expr (e.g. Sin[-x] --> -Sin[x])." 48 Csc[x_] :> 1/Sin[x] /; simplify[Sin[x] != 0], 59 Sin[(n_?Negative) x_ + y_] :> -Sin[-n x - y] /; 90 a_. Sin[x_] + a_. Sin[y_] :> 2 a Sin[x/2+y/2] Cos[x/2-y/2], 91 a_. Sin[x_] + b_. Sin[y_] :> 2 a Sin[x/2-y/2] Cos[x/2+y/2] /; a+b == 0, 95 a_. Sin[x_] Cos[y_] + a_. Sin[y_] Cos[x_] :> a Sin[x + y], 96 a_. Sin[x_] Cos[y_] + b_. Sin[y_] Cos[x_] :> a Sin[x - y] /; a+b == 0, 108 Sin[x_ + y_] :> Sin[x] Cos[y] + Sin[y] Cos[x], 109 Cos[x_ + y_] :> Cos[x] Cos[y] - Sin[y] Sin[x], 111 If[n<0, -Sin[-n x], Sin[x] Cos[(n-1) x] + Cos[x] Sin[(n-1) x]], [all …]

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