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Searched refs:Sinh (Results 1 – 25 of 1738) sorted by relevance

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/dports/math/reduce/Reduce-svn5758-src/contrib/rubi-red/mathematicatests/
H A DHyperbolicSineFunctions.m65 {Sinh[x]^(3/2)/x^3, x, 1, (3/8)*Int[1/(x*Sqrt[Sinh[x]]), x] + (9/8)*Int[Sinh[x]^(3/2)/x, x] - (3*Co…
76 {1/(a*Sinh[x]^2)^(1/2), x, 2, -((ArcCoth[Cosh[x]]*Sinh[x])/Sqrt[a*Sinh[x]^2])}
82 …Sinh[x]^3)^(5/2),x, 7, (2*a^2*Csch[x]^2*Sqrt[a*Sinh[x]^3]*(195*I*EllipticF[Pi/4 - (I*x)/2, 2]*Sqrt…
85 {1/(a*Sinh[x]^3)^(1/2), x, 4, -((2*Sinh[x]*(Cosh[x] - (I*EllipticE[Pi/4 - (I*x)/2, 2]*Sinh[x])/Sqrt…
87 …Sinh[x]^3)^(5/2),x, 7, -((2*Csch[x]^5*(45*Cosh[x] - 11*Sinh[x]^2*(5*Cosh[x] - 7*Sinh[x]^2*(Cosh[x]…
91 …Sinh[x]^4)^(5/2),x, 6, (63/256)*a^2*Coth[x]*Sqrt[a*Sinh[x]^4] - (63/256)*a^2*x*Csch[x]^2*Sqrt[a*Si…
92 …Sinh[x]^4)^(3/2),x, 4, (5/16)*a*Coth[x]*Sqrt[a*Sinh[x]^4] - (5/16)*a*x*Csch[x]^2*Sqrt[a*Sinh[x]^4]…
94 {1/(a*Sinh[x]^4)^(1/2), x, 2, -((Cosh[x]*Sinh[x])/Sqrt[a*Sinh[x]^4])}
521 {x/Sinh[x]^(3/2) - x*Sqrt[Sinh[x]], x, 2, -((2*x*Cosh[x])/Sqrt[Sinh[x]]) + 4*Sqrt[Sinh[x]]}
523 …Sinh[x]^(7/2) + (3/5)*x*Sqrt[Sinh[x]], x, 3, -((2*x*Cosh[x])/(5*Sinh[x]^(5/2))) - 4/(15*Sinh[x]^(3…
[all …]
H A DTwoHyperbolicFunctions.m465 {Sinh[2*x]*Sinh[x], x, 3, (2*Sinh[x]^3)/3}
466 {Sinh[3*x]*Sinh[x], x, 3, (-(1/4))*Sinh[2*x] + (1/8)*Sinh[4*x]}
467 {Sinh[4*x]*Sinh[x], x, 3, (-(1/6))*Sinh[3*x] + (1/10)*Sinh[5*x]}
468 {Sinh[m*x]*Sinh[x], x, 3, -(Sinh[(1 - m)*x]/(2*(1 - m))) + Sinh[(1 + m)*x]/(2*(1 + m))}
480 {Tanh[3*x]*Sinh[x], x, 3, (-(1/3))*ArcTan[(3*Sinh[x])/(1 - 2*Sinh[x]^2)] + Sinh[x]}
489 {Coth[2*x]*Sinh[x], x, 4, (-(1/2))*ArcTan[Sinh[x]] + Sinh[x]}
595 {Sinh[x]/(I + Sinh[x]), x, 2, x + (I*Cosh[x])/(1 - I*Sinh[x])}
609 {Cosh[x]^3/(I + Sinh[x]), x, 2, (-I)*Sinh[x] + Sinh[x]^2/2}
621 {Tanh[x]^3/(I + Sinh[x]), x, 7, (3/8)*ArcTan[Sinh[x]] + 1/(8*(I - Sinh[x])) + I/(8*(I + Sinh[x])^2)…
1097 {Coth[x]/(I + Sinh[x])^2, x, 5, -Log[Sinh[x]] + Log[I + Sinh[x]] - I/(I + Sinh[x])}
[all …]
H A DHyperbolicIntegralFunctions.m61 …Sinh[b*x]*SinhIntegral[b*x]/x^3, x, 16, b^2*CoshIntegral[2*b*x] - (b*Cosh[b*x]*Sinh[b*x])/(2*x) - …
65 {x*Sinh[b*x]*SinhIntegral[b*x], x, 10, CoshIntegral[2*b*x]/(2*b^2) - Log[x]/(2*b^2) - Sinh[b*x]^2/(…
66 …Sinh[b*x]*SinhIntegral[b*x], x, 12, -((5*x)/(4*b^2)) + (5*Cosh[b*x]*Sinh[b*x])/(4*b^3) - (x*Sinh[b…
67 …Sinh[b*x]*SinhIntegral[b*x], x, 19, -(x^2/b^2) + (3*CoshIntegral[2*b*x])/b^4 - (3*Log[x])/b^4 + (2…
85 {Sinh[a + b*x]*SinhIntegral[c + d*x]/x, x, 0, Int[(Sinh[a + b*x]*SinhIntegral[c + d*x])/x, x]}
164 …Sinh[b*x]*CoshIntegral[b*x]/x^3, x, 14, -(b/(4*x)) - (b*Cosh[2*b*x])/(2*x) + (1/2)*b^2*Int[(CoshIn…
165 {Sinh[b*x]*CoshIntegral[b*x]/x^2, x, 8, (1/2)*b*CoshIntegral[b*x]^2 + b*CoshIntegral[2*b*x] - (Cosh…
166 {Sinh[b*x]*CoshIntegral[b*x]/x, x, 0, Int[(CoshIntegral[b*x]*Sinh[b*x])/x, x]}
168 {x*Sinh[b*x]*CoshIntegral[b*x], x, 8, -(x/(2*b)) + (CoshIntegral[b*x]*(b*x*Cosh[b*x] - Sinh[b*x]))/…
169 …Sinh[b*x]*CoshIntegral[b*x], x, 14, -(x^2/(4*b)) + Cosh[b*x]^2/(4*b^3) - CoshIntegral[2*b*x]/b^3 -…
[all …]
H A DHyperbolicFunctions.m19 (* Integrands of the form Sinh[x]^m/(a*Cosh[x]+b*Sinh[x]) *)
68 {Sinh[x]/(a*Cosh[x] + b*Sinh[x])^3, x, 3, -(a/(2*(a^2 - b^2)*(a*Cosh[x] + b*Sinh[x])^2)) - (b*Sinh[…
130 (* Integrands of the form Sinh[x]^m/(a+b*Sinh[x]*c*Sinh[x]^2) where m is an integer *)
136 {(a + b*Sinh[x])/(b^2 - 2*a*b*Sinh[x] + a^2*Sinh[x]^2), x, 2, Cosh[x]/(b - a*Sinh[x])}
158 {(x*Cosh[x] - Sinh[x])/(x - Sinh[x])^2, x, -7, x/(x - Sinh[x])}
276 {(Cosh[x] - Sinh[x])/(Cosh[x] + Sinh[x]), x, 2, (-(1/2))*(Cosh[x] - Sinh[x])^2}
477 {Sinh[x]^3*(a + b*Sinh[x]^2)^3*Cosh[x], x, 4, -((a*(a + b*Sinh[x]^2)^4)/(40*b^2)) + (Sinh[x]^2*(a +…
480 {Cosh[x]*Sinh[x]*Sqrt[a + b*Sinh[x]^2], x, 3, (a + b*Sinh[x]^2)^(3/2)/(3*b)}
488 {(Cosh[x] - Sinh[x])/(Cosh[x] + Sinh[x]), x, 2, (-(1/2))*(Cosh[x] - Sinh[x])^2}
489 {Sinh[x]*(Cosh[x] + Sinh[x]), x, 5, -(x/2) + (1/2)*Cosh[x]*Sinh[x] + Sinh[x]^2/2}
[all …]
H A DHyperbolicCosineFunctions.m14 {Cosh[a + b*x]^3, x, 2, Sinh[a + b*x]/b + Sinh[a + b*x]^3/(3*b)}
16 {Cosh[a + b*x]^5, x, 2, Sinh[a + b*x]/b + (2*Sinh[a + b*x]^3)/(3*b) + Sinh[a + b*x]^5/(5*b)}
110 … (2*Sech[x]^5*(45*Sinh[x] + 11*Cosh[x]^2*(5*Sinh[x] + 7*Cosh[x]^2*(Sinh[x] + 3*Cosh[x]^2*(I*Sqrt[C…
127 …Sinh[c + d*x])/d + (4*a*b^3*Sinh[c + d*x])/d + (3*a^2*b^2*Cosh[c + d*x]*Sinh[c + d*x])/d + (3*b^4*…
128 …+ (3/2)*a*b^2*x + (3*a^2*b*Sinh[c + d*x])/d + (b^3*Sinh[c + d*x])/d + (3*a*b^2*Cosh[c + d*x]*Sinh[…
299 {1/Sqrt[1 - Cosh[x]^2], x, 3, -((ArcCoth[Cosh[x]]*Sinh[x])/Sqrt[-Sinh[x]^2])}
300 {1/Sqrt[-1 + Cosh[x]^2], x, 3, -((ArcCoth[Cosh[x]]*Sinh[x])/Sqrt[Sinh[x]^2])}
448 {x*Cosh[a + b*x^2]^3, x, 3, Sinh[a + b*x^2]/(2*b) + Sinh[a + b*x^2]^3/(6*b)}
455 {x*Cosh[a + b*x^2]^7, x, 3, Sinh[a + b*x^2]/(2*b) + Sinh[a + b*x^2]^3/(2*b) + (3*Sinh[a + b*x^2]^5)…
514 {Cosh[a + b*Log[c*x^n]]^5/x, x, 3, Sinh[a + b*Log[c*x^n]]/(b*n) + (2*Sinh[a + b*Log[c*x^n]]^3)/(3*b…
[all …]
/dports/math/reduce/Reduce-svn5758-src/packages/rubi_red/tests/HyperbolicFunctions/
H A DHyperbolicSineFunctions.m65 {Sinh[x]^(3/2)/x^3, x, 1, (3/8)*Int[1/(x*Sqrt[Sinh[x]]), x] + (9/8)*Int[Sinh[x]^(3/2)/x, x] - (3*Co…
76 {1/(a*Sinh[x]^2)^(1/2), x, 2, -((ArcCoth[Cosh[x]]*Sinh[x])/Sqrt[a*Sinh[x]^2])}
82 …Sinh[x]^3)^(5/2),x, 7, (2*a^2*Csch[x]^2*Sqrt[a*Sinh[x]^3]*(195*I*EllipticF[Pi/4 - (I*x)/2, 2]*Sqrt…
85 {1/(a*Sinh[x]^3)^(1/2), x, 4, -((2*Sinh[x]*(Cosh[x] - (I*EllipticE[Pi/4 - (I*x)/2, 2]*Sinh[x])/Sqrt…
87 …Sinh[x]^3)^(5/2),x, 7, -((2*Csch[x]^5*(45*Cosh[x] - 11*Sinh[x]^2*(5*Cosh[x] - 7*Sinh[x]^2*(Cosh[x]…
91 …Sinh[x]^4)^(5/2),x, 6, (63/256)*a^2*Coth[x]*Sqrt[a*Sinh[x]^4] - (63/256)*a^2*x*Csch[x]^2*Sqrt[a*Si…
92 …Sinh[x]^4)^(3/2),x, 4, (5/16)*a*Coth[x]*Sqrt[a*Sinh[x]^4] - (5/16)*a*x*Csch[x]^2*Sqrt[a*Sinh[x]^4]…
94 {1/(a*Sinh[x]^4)^(1/2), x, 2, -((Cosh[x]*Sinh[x])/Sqrt[a*Sinh[x]^4])}
521 {x/Sinh[x]^(3/2) - x*Sqrt[Sinh[x]], x, 2, -((2*x*Cosh[x])/Sqrt[Sinh[x]]) + 4*Sqrt[Sinh[x]]}
523 …Sinh[x]^(7/2) + (3/5)*x*Sqrt[Sinh[x]], x, 3, -((2*x*Cosh[x])/(5*Sinh[x]^(5/2))) - 4/(15*Sinh[x]^(3…
[all …]
H A DTwoHyperbolicFunctions.m465 {Sinh[2*x]*Sinh[x], x, 3, (2*Sinh[x]^3)/3}
466 {Sinh[3*x]*Sinh[x], x, 3, (-(1/4))*Sinh[2*x] + (1/8)*Sinh[4*x]}
467 {Sinh[4*x]*Sinh[x], x, 3, (-(1/6))*Sinh[3*x] + (1/10)*Sinh[5*x]}
468 {Sinh[m*x]*Sinh[x], x, 3, -(Sinh[(1 - m)*x]/(2*(1 - m))) + Sinh[(1 + m)*x]/(2*(1 + m))}
480 {Tanh[3*x]*Sinh[x], x, 3, (-(1/3))*ArcTan[(3*Sinh[x])/(1 - 2*Sinh[x]^2)] + Sinh[x]}
489 {Coth[2*x]*Sinh[x], x, 4, (-(1/2))*ArcTan[Sinh[x]] + Sinh[x]}
595 {Sinh[x]/(I + Sinh[x]), x, 2, x + (I*Cosh[x])/(1 - I*Sinh[x])}
609 {Cosh[x]^3/(I + Sinh[x]), x, 2, (-I)*Sinh[x] + Sinh[x]^2/2}
621 {Tanh[x]^3/(I + Sinh[x]), x, 7, (3/8)*ArcTan[Sinh[x]] + 1/(8*(I - Sinh[x])) + I/(8*(I + Sinh[x])^2)…
1097 {Coth[x]/(I + Sinh[x])^2, x, 5, -Log[Sinh[x]] + Log[I + Sinh[x]] - I/(I + Sinh[x])}
[all …]
H A DHyperbolicFunctions.m19 (* Integrands of the form Sinh[x]^m/(a*Cosh[x]+b*Sinh[x]) *)
68 {Sinh[x]/(a*Cosh[x] + b*Sinh[x])^3, x, 3, -(a/(2*(a^2 - b^2)*(a*Cosh[x] + b*Sinh[x])^2)) - (b*Sinh[…
130 (* Integrands of the form Sinh[x]^m/(a+b*Sinh[x]*c*Sinh[x]^2) where m is an integer *)
136 {(a + b*Sinh[x])/(b^2 - 2*a*b*Sinh[x] + a^2*Sinh[x]^2), x, 2, Cosh[x]/(b - a*Sinh[x])}
158 {(x*Cosh[x] - Sinh[x])/(x - Sinh[x])^2, x, -7, x/(x - Sinh[x])}
276 {(Cosh[x] - Sinh[x])/(Cosh[x] + Sinh[x]), x, 2, (-(1/2))*(Cosh[x] - Sinh[x])^2}
477 {Sinh[x]^3*(a + b*Sinh[x]^2)^3*Cosh[x], x, 4, -((a*(a + b*Sinh[x]^2)^4)/(40*b^2)) + (Sinh[x]^2*(a +…
480 {Cosh[x]*Sinh[x]*Sqrt[a + b*Sinh[x]^2], x, 3, (a + b*Sinh[x]^2)^(3/2)/(3*b)}
488 {(Cosh[x] - Sinh[x])/(Cosh[x] + Sinh[x]), x, 2, (-(1/2))*(Cosh[x] - Sinh[x])^2}
489 {Sinh[x]*(Cosh[x] + Sinh[x]), x, 5, -(x/2) + (1/2)*Cosh[x]*Sinh[x] + Sinh[x]^2/2}
[all …]
H A DHyperbolicCosineFunctions.m14 {Cosh[a + b*x]^3, x, 2, Sinh[a + b*x]/b + Sinh[a + b*x]^3/(3*b)}
16 {Cosh[a + b*x]^5, x, 2, Sinh[a + b*x]/b + (2*Sinh[a + b*x]^3)/(3*b) + Sinh[a + b*x]^5/(5*b)}
110 … (2*Sech[x]^5*(45*Sinh[x] + 11*Cosh[x]^2*(5*Sinh[x] + 7*Cosh[x]^2*(Sinh[x] + 3*Cosh[x]^2*(I*Sqrt[C…
127 …Sinh[c + d*x])/d + (4*a*b^3*Sinh[c + d*x])/d + (3*a^2*b^2*Cosh[c + d*x]*Sinh[c + d*x])/d + (3*b^4*…
128 …+ (3/2)*a*b^2*x + (3*a^2*b*Sinh[c + d*x])/d + (b^3*Sinh[c + d*x])/d + (3*a*b^2*Cosh[c + d*x]*Sinh[…
299 {1/Sqrt[1 - Cosh[x]^2], x, 3, -((ArcCoth[Cosh[x]]*Sinh[x])/Sqrt[-Sinh[x]^2])}
300 {1/Sqrt[-1 + Cosh[x]^2], x, 3, -((ArcCoth[Cosh[x]]*Sinh[x])/Sqrt[Sinh[x]^2])}
448 {x*Cosh[a + b*x^2]^3, x, 3, Sinh[a + b*x^2]/(2*b) + Sinh[a + b*x^2]^3/(6*b)}
455 {x*Cosh[a + b*x^2]^7, x, 3, Sinh[a + b*x^2]/(2*b) + Sinh[a + b*x^2]^3/(2*b) + (3*Sinh[a + b*x^2]^5)…
514 {Cosh[a + b*Log[c*x^n]]^5/x, x, 3, Sinh[a + b*Log[c*x^n]]/(b*n) + (2*Sinh[a + b*Log[c*x^n]]^3)/(3*b…
[all …]
/dports/math/reduce/Reduce-svn5758-src/contrib/rubi-red/rubi4/IntegrationProblems/MathematicaSyntaxFiles/HyperbolicFunctions/
H A DHyperbolicSineFunctions.m65 {Sinh[x]^(3/2)/x^3, x, 1, (3/8)*Int[1/(x*Sqrt[Sinh[x]]), x] + (9/8)*Int[Sinh[x]^(3/2)/x, x] - (3*Co…
76 {1/(a*Sinh[x]^2)^(1/2), x, 2, -((ArcCoth[Cosh[x]]*Sinh[x])/Sqrt[a*Sinh[x]^2])}
82 …Sinh[x]^3)^(5/2),x, 7, (2*a^2*Csch[x]^2*Sqrt[a*Sinh[x]^3]*(195*I*EllipticF[Pi/4 - (I*x)/2, 2]*Sqrt…
85 {1/(a*Sinh[x]^3)^(1/2), x, 4, -((2*Sinh[x]*(Cosh[x] - (I*EllipticE[Pi/4 - (I*x)/2, 2]*Sinh[x])/Sqrt…
87 …Sinh[x]^3)^(5/2),x, 7, -((2*Csch[x]^5*(45*Cosh[x] - 11*Sinh[x]^2*(5*Cosh[x] - 7*Sinh[x]^2*(Cosh[x]…
91 …Sinh[x]^4)^(5/2),x, 6, (63/256)*a^2*Coth[x]*Sqrt[a*Sinh[x]^4] - (63/256)*a^2*x*Csch[x]^2*Sqrt[a*Si…
92 …Sinh[x]^4)^(3/2),x, 4, (5/16)*a*Coth[x]*Sqrt[a*Sinh[x]^4] - (5/16)*a*x*Csch[x]^2*Sqrt[a*Sinh[x]^4]…
94 {1/(a*Sinh[x]^4)^(1/2), x, 2, -((Cosh[x]*Sinh[x])/Sqrt[a*Sinh[x]^4])}
521 {x/Sinh[x]^(3/2) - x*Sqrt[Sinh[x]], x, 2, -((2*x*Cosh[x])/Sqrt[Sinh[x]]) + 4*Sqrt[Sinh[x]]}
523 …Sinh[x]^(7/2) + (3/5)*x*Sqrt[Sinh[x]], x, 3, -((2*x*Cosh[x])/(5*Sinh[x]^(5/2))) - 4/(15*Sinh[x]^(3…
[all …]
H A DTwoHyperbolicFunctions.m465 {Sinh[2*x]*Sinh[x], x, 3, (2*Sinh[x]^3)/3}
466 {Sinh[3*x]*Sinh[x], x, 3, (-(1/4))*Sinh[2*x] + (1/8)*Sinh[4*x]}
467 {Sinh[4*x]*Sinh[x], x, 3, (-(1/6))*Sinh[3*x] + (1/10)*Sinh[5*x]}
468 {Sinh[m*x]*Sinh[x], x, 3, -(Sinh[(1 - m)*x]/(2*(1 - m))) + Sinh[(1 + m)*x]/(2*(1 + m))}
480 {Tanh[3*x]*Sinh[x], x, 3, (-(1/3))*ArcTan[(3*Sinh[x])/(1 - 2*Sinh[x]^2)] + Sinh[x]}
489 {Coth[2*x]*Sinh[x], x, 4, (-(1/2))*ArcTan[Sinh[x]] + Sinh[x]}
595 {Sinh[x]/(I + Sinh[x]), x, 2, x + (I*Cosh[x])/(1 - I*Sinh[x])}
609 {Cosh[x]^3/(I + Sinh[x]), x, 2, (-I)*Sinh[x] + Sinh[x]^2/2}
621 {Tanh[x]^3/(I + Sinh[x]), x, 7, (3/8)*ArcTan[Sinh[x]] + 1/(8*(I - Sinh[x])) + I/(8*(I + Sinh[x])^2)…
1097 {Coth[x]/(I + Sinh[x])^2, x, 5, -Log[Sinh[x]] + Log[I + Sinh[x]] - I/(I + Sinh[x])}
[all …]
H A DHyperbolicFunctions.m19 (* Integrands of the form Sinh[x]^m/(a*Cosh[x]+b*Sinh[x]) *)
68 {Sinh[x]/(a*Cosh[x] + b*Sinh[x])^3, x, 3, -(a/(2*(a^2 - b^2)*(a*Cosh[x] + b*Sinh[x])^2)) - (b*Sinh[…
130 (* Integrands of the form Sinh[x]^m/(a+b*Sinh[x]*c*Sinh[x]^2) where m is an integer *)
136 {(a + b*Sinh[x])/(b^2 - 2*a*b*Sinh[x] + a^2*Sinh[x]^2), x, 2, Cosh[x]/(b - a*Sinh[x])}
158 {(x*Cosh[x] - Sinh[x])/(x - Sinh[x])^2, x, -7, x/(x - Sinh[x])}
276 {(Cosh[x] - Sinh[x])/(Cosh[x] + Sinh[x]), x, 2, (-(1/2))*(Cosh[x] - Sinh[x])^2}
477 {Sinh[x]^3*(a + b*Sinh[x]^2)^3*Cosh[x], x, 4, -((a*(a + b*Sinh[x]^2)^4)/(40*b^2)) + (Sinh[x]^2*(a +…
480 {Cosh[x]*Sinh[x]*Sqrt[a + b*Sinh[x]^2], x, 3, (a + b*Sinh[x]^2)^(3/2)/(3*b)}
488 {(Cosh[x] - Sinh[x])/(Cosh[x] + Sinh[x]), x, 2, (-(1/2))*(Cosh[x] - Sinh[x])^2}
489 {Sinh[x]*(Cosh[x] + Sinh[x]), x, 5, -(x/2) + (1/2)*Cosh[x]*Sinh[x] + Sinh[x]^2/2}
[all …]
H A DHyperbolicCosineFunctions.m14 {Cosh[a + b*x]^3, x, 2, Sinh[a + b*x]/b + Sinh[a + b*x]^3/(3*b)}
16 {Cosh[a + b*x]^5, x, 2, Sinh[a + b*x]/b + (2*Sinh[a + b*x]^3)/(3*b) + Sinh[a + b*x]^5/(5*b)}
110 … (2*Sech[x]^5*(45*Sinh[x] + 11*Cosh[x]^2*(5*Sinh[x] + 7*Cosh[x]^2*(Sinh[x] + 3*Cosh[x]^2*(I*Sqrt[C…
127 …Sinh[c + d*x])/d + (4*a*b^3*Sinh[c + d*x])/d + (3*a^2*b^2*Cosh[c + d*x]*Sinh[c + d*x])/d + (3*b^4*…
128 …+ (3/2)*a*b^2*x + (3*a^2*b*Sinh[c + d*x])/d + (b^3*Sinh[c + d*x])/d + (3*a*b^2*Cosh[c + d*x]*Sinh[…
299 {1/Sqrt[1 - Cosh[x]^2], x, 3, -((ArcCoth[Cosh[x]]*Sinh[x])/Sqrt[-Sinh[x]^2])}
300 {1/Sqrt[-1 + Cosh[x]^2], x, 3, -((ArcCoth[Cosh[x]]*Sinh[x])/Sqrt[Sinh[x]^2])}
448 {x*Cosh[a + b*x^2]^3, x, 3, Sinh[a + b*x^2]/(2*b) + Sinh[a + b*x^2]^3/(6*b)}
455 {x*Cosh[a + b*x^2]^7, x, 3, Sinh[a + b*x^2]/(2*b) + Sinh[a + b*x^2]^3/(2*b) + (3*Sinh[a + b*x^2]^5)…
514 {Cosh[a + b*Log[c*x^n]]^5/x, x, 3, Sinh[a + b*Log[c*x^n]]/(b*n) + (2*Sinh[a + b*Log[c*x^n]]^3)/(3*b…
[all …]
/dports/math/reduce/Reduce-svn5758-src/packages/rubi_red/tests4/HyperbolicFunctions/
H A DHyperbolicSineFunctions.m113 …Sinh[x]^3)^(1/2), x, 4, -((2*I*EllipticE[Pi/4 - (I*x)/2, 2]*(I*Sinh[x])^(3/2))/Sqrt[a*Sinh[x]^3]) …
122 …Sinh[x]^4)^(5/2),x, 6, (63/256)*a^2*Coth[x]*Sqrt[a*Sinh[x]^4] - (63/256)*a^2*x*Csch[x]^2*Sqrt[a*Si…
123 …Sinh[x]^4)^(3/2),x, 4, (5/16)*a*Coth[x]*Sqrt[a*Sinh[x]^4] - (5/16)*a*x*Csch[x]^2*Sqrt[a*Sinh[x]^4]…
147 {Sinh[x]^3/(I + Sinh[x]), x, 3, -((3*x)/2) - 2*I*Cosh[x] + (3/2)*Cosh[x]*Sinh[x] - (Cosh[x]*Sinh[x]…
149 {Sinh[x]^1/(I + Sinh[x]), x, 2, x - Cosh[x]/(I + Sinh[x])}
156 …Sinh[x]^4/(I + Sinh[x])^2, x, 5, -((7*x)/2) - (16/3)*I*Cosh[x] + (7/2)*Cosh[x]*Sinh[x] - (Cosh[x]*…
157 {Sinh[x]^3/(I + Sinh[x])^2, x, 4, -2*I*x + (4*Cosh[x])/3 - (Cosh[x]*Sinh[x]^2)/(3*(I + Sinh[x])^2) …
255 {Cosh[x]^7/(I + Sinh[x]), x, 4, (-I)*Sinh[x] + Sinh[x]^2/2 - (2/3)*I*Sinh[x]^3 + Sinh[x]^4/2 - (1/5…
257 {Cosh[x]^5/(I + Sinh[x]), x, 4, (-I)*Sinh[x] + Sinh[x]^2/2 - (1/3)*I*Sinh[x]^3 + Sinh[x]^4/4}
259 {Cosh[x]^3/(I + Sinh[x]), x, 3, (-I)*Sinh[x] + Sinh[x]^2/2}
[all …]
H A DTwoHyperbolicFunctions.m109 {Sinh[a + b*x]^3*Tanh[a + b*x], x, 3, ArcTan[Sinh[a + b*x]]/b - Sinh[a + b*x]/b + Sinh[a + b*x]^3/(…
779 {Sinh[2*x]*Sinh[x], x, 2, (2*Sinh[x]^3)/3}
780 {Sinh[3*x]*Sinh[x], x, 3, (-(1/4))*Sinh[2*x] + (1/8)*Sinh[4*x]}
781 {Sinh[4*x]*Sinh[x], x, 3, (-(1/6))*Sinh[3*x] + (1/10)*Sinh[5*x]}
782 {Sinh[m*x]*Sinh[x], x, 3, -(Sinh[(1 - m)*x]/(2*(1 - m))) + Sinh[(1 + m)*x]/(2*(1 + m))}
791 {Tanh[2*x]*Sinh[x], x, 4, -(ArcTan[Sqrt[2]*Sinh[x]]/Sqrt[2]) + Sinh[x]}
792 {Tanh[3*x]*Sinh[x], x, 5, (-(1/3))*ArcTan[Sinh[x]] - (1/3)*ArcTan[2*Sinh[x]] + Sinh[x]}
800 {Coth[2*x]*Sinh[x], x, 3, (-(1/2))*ArcTan[Sinh[x]] + Sinh[x]}
802 {Coth[4*x]*Sinh[x], x, 6, (-(1/4))*ArcTan[Sinh[x]] - ArcTan[Sqrt[2]*Sinh[x]]/(2*Sqrt[2]) + Sinh[x]}
804 {Coth[6*x]*Sinh[x], x, 9, (-(1/6))*ArcTan[Sinh[x]] - (1/6)*ArcTan[2*Sinh[x]] - ArcTan[(2*Sinh[x])/S…
[all …]
H A DHyperbolicFunctions.m19 {Sinh[x]/(a*Cosh[x] + b*Sinh[x]), x, 2, -((b*x)/(a^2 - b^2)) + (a*Log[a*Cosh[x] + b*Sinh[x]])/(a^2 …
76 {Sinh[x]/(1 + Cosh[x] + Sinh[x]), x, 1, x/2 + Cosh[x]/2 - Sinh[x]/2}
123 {(a + b*Sinh[x])/(b^2 - 2*a*b*Sinh[x] + a^2*Sinh[x]^2), x, 2, Cosh[x]/(b - a*Sinh[x])}
144 (* {(x*Cosh[x] - Sinh[x])/(x - Sinh[x])^2, x, -7, x/(x - Sinh[x])} *)
258 {(Cosh[x] - Sinh[x])/(Cosh[x] + Sinh[x]), x, 4, -(Cosh[x]/(Cosh[x] + Sinh[x]))}
259 {(Cosh[x] - I*Sinh[x])/(Cosh[x] + I*Sinh[x]), x, 1, (-I)*Log[Cosh[x] + I*Sinh[x]]}
459 {Sinh[x]^3*(a + b*Sinh[x]^2)^3*Cosh[x], x, 4, -((a*(a + b*Sinh[x]^2)^4)/(8*b^2)) + (a + b*Sinh[x]^2…
462 {Cosh[x]*Sinh[x]*Sqrt[a + b*Sinh[x]^2], x, 2, (a + b*Sinh[x]^2)^(3/2)/(3*b)}
469 {(Cosh[x] - Sinh[x])/(Cosh[x] + Sinh[x]), x, 4, -(Cosh[x]/(Cosh[x] + Sinh[x]))}
470 {Sinh[x]*(Cosh[x] + Sinh[x]), x, 4, -(x/2) + (1/2)*Cosh[x]*Sinh[x] + Sinh[x]^2/2}
[all …]
H A DHyperbolicCosineFunctions.m17 {Cosh[a + b*x]^3, x, 2, Sinh[a + b*x]/b + Sinh[a + b*x]^3/(3*b)}
19 {Cosh[a + b*x]^5, x, 2, Sinh[a + b*x]/b + (2*Sinh[a + b*x]^3)/(3*b) + Sinh[a + b*x]^5/(5*b)}
112 {Sinh[x]^2/(1 + Cosh[x])^2, x, 2, x - (2*Sinh[x])/(1 + Cosh[x])}
126 {Sinh[x]^8/(a + a*Cosh[x]), x, 4, (5*x)/(16*a) - (5*Cosh[x]*Sinh[x])/(16*a) + (5*Cosh[x]*Sinh[x]^3)…
128 {Sinh[x]^6/(a + a*Cosh[x]), x, 3, -((3*x)/(8*a)) + (3*Cosh[x]*Sinh[x])/(8*a) - (Cosh[x]*Sinh[x]^3)/…
130 {Sinh[x]^4/(a + a*Cosh[x]), x, 2, x/(2*a) - (Cosh[x]*Sinh[x])/(2*a) + Sinh[x]^3/(3*a)}
132 {Sinh[x]^2/(a + a*Cosh[x]), x, 2, -(x/a) + Sinh[x]/a}
181 …h[x]), x, 4, -((3*x)/(2*a)) + (4*Sinh[x])/a - (3*Cosh[x]*Sinh[x])/(2*a) - (Cosh[x]^3*Sinh[x])/(a +…
366 {Tanh[x]/Sqrt[1 - Cosh[x]^2], x, 2, (ArcTan[Sinh[x]]*Sinh[x])/Sqrt[-Sinh[x]^2]}
798 {x*Cosh[a + b*x^2]^7, x, 3, Sinh[a + b*x^2]/(2*b) + Sinh[a + b*x^2]^3/(2*b) + (3*Sinh[a + b*x^2]^5)…
[all …]
H A Dcosh(c+d x)^m (a+b cosh(c+d x))^n.m16 …Sinh[c + d*x])/d + (35*b*Cosh[c + d*x]*Sinh[c + d*x])/(128*d) + (35*b*Cosh[c + d*x]^3*Sinh[c + d*x…
17 …Sinh[c + d*x])/d + (5*a*Cosh[c + d*x]*Sinh[c + d*x])/(16*d) + (5*a*Cosh[c + d*x]^3*Sinh[c + d*x])/…
18 …Sinh[c + d*x])/d + (5*b*Cosh[c + d*x]*Sinh[c + d*x])/(16*d) + (5*b*Cosh[c + d*x]^3*Sinh[c + d*x])/…
19 … + (b*Sinh[c + d*x])/d + (3*a*Cosh[c + d*x]*Sinh[c + d*x])/(8*d) + (a*Cosh[c + d*x]^3*Sinh[c + d*x…
20 …x, 5, (3*b*x)/8 + (a*Sinh[c + d*x])/d + (3*b*Cosh[c + d*x]*Sinh[c + d*x])/(8*d) + (b*Cosh[c + d*x]…
21 …*(a + b*Cosh[c + d*x]), x, 4, (a*x)/2 + (b*Sinh[c + d*x])/d + (a*Cosh[c + d*x]*Sinh[c + d*x])/(2*d…
32 …Sinh[c + d*x])/d + ((6*a^2 + 5*b^2)*Cosh[c + d*x]*Sinh[c + d*x])/(16*d) + ((6*a^2 + 5*b^2)*Cosh[c …
33 …Sinh[c + d*x])/(5*d) + (3*a*b*Cosh[c + d*x]*Sinh[c + d*x])/(4*d) + (a*b*Cosh[c + d*x]^3*Sinh[c + d…
34 …*x + (2*a*b*Sinh[c + d*x])/d + ((4*a^2 + 3*b^2)*Cosh[c + d*x]*Sinh[c + d*x])/(8*d) + (b^2*Cosh[c +…
35 …, x, 3, a*b*x + ((3*a^2 + 2*b^2)*Sinh[c + d*x])/(3*d) + (a*b*Cosh[c + d*x]*Sinh[c + d*x])/d + (b^2…
[all …]
/dports/math/reduce/Reduce-svn5758-src/packages/rubi_red/rubi-rules/HyperbolicFunctions/
H A DRationalFunctionsOfHyperbolicSinesAndCosines.m34 …\[Integral]1/(a Cosh[c+d x]+b Sinh[c+d x])^2 \[DifferentialD]x \[LongRightArrow] (Sinh[c+d x]/(a…
43 Sinh[c+d*x]/(a*d*(a*Cosh[c+d*x]+b*Sinh[c+d*x])) /;
101 (*(((b Cosh[c+d x]+a Sinh[c+d x]) (a Cosh[c+d x]+b Sinh[c+d x])^(n-1))/(d n))+*)
111 (b*Cosh[c+d*x]+a*Sinh[c+d*x])*(a*Cosh[c+d*x]+b*Sinh[c+d*x])^(n-1)/(d*n) +
158 (*Basis: (Cosh[z] Sinh[z])/(a Cosh[z]+b Sinh[z])=-((b Cosh[z])/(a^2-b^2))+(a Sinh[z])/(a^2-b^2)+(a …
193 (*Basis: Sinh[z]^2/(a Cosh[z]+b Sinh[z])=-((b Sinh[z])/(a^2-b^2))+(a Cosh[z])/(a^2-b^2)-a^2/((a^2-b…
227 (*Basis: Cosh[z]^2/(a Cosh[z]+b Sinh[z])=(a Cosh[z])/(a^2-b^2)-(b Sinh[z])/(a^2-b^2)-b^2/((a^2-b^2)…
330 -(c+a*Sinh[d+e*x])/(c*e*(c*Cosh[d+e*x]+b*Sinh[d+e*x])) /;
421 (*Basis: a+b Cosh[z]+c Sinh[z]=a-I Sqrt[b^2-c^2] Sinh[z+I ArcTan[I c,b]]*)
451 (*Basis: a+b Cosh[z]+c Sinh[z]=a-I Sqrt[b^2-c^2] Sinh[z+I ArcTan[I c,b]]*)
[all …]
H A DTwoHyperbolicFunctions.m4 (*\[Integral](x (A+B Sinh[c+d x]))/(a+b Sinh[c+d x])^2 \[DifferentialD]x*)
400 (*Basis: Sinh[v] Cosh[w]=1/2 Sinh[v+w]+1/2 Sinh[v-w]*)
431 (*Basis: Sinh[v] Sinh[w]=1/2 Cosh[v+w]-1/2 Cosh[v-w]*)
447 Int[u_.*Sinh[v_]*Sinh[w_],x_Symbol] :=
513 (*Basis: Sinh[v] Coth[w]=Cosh[v]+Sinh[v-w] Csch[w]*)
535 (*Basis: Cosh[v] Tanh[w]=Sinh[v]-Sinh[v-w] Sech[w]*)
553 (*Basis: Sinh[v] Sech[w]=Cosh[v-w] Tanh[w]+Sinh[v-w]*)
709 …\[Element]\[DoubleStruckCapitalZ], then Sinh[z]^m Cosh[z]^n=Sinh[z]^m (1+Sinh[z]^2)^((n-1)/2) Deri…
957 (*Basis: Sinh[z] Cosh[z]=1/2 Sinh[2 z]*)
987 (*Basis: Sinh[z] Cosh[z]=1/2 Sinh[2 z]*)
[all …]
H A DHyperbolicSineFunctions.m90 …Sinh[c+d x])^2 \[DifferentialD]x \[LongRightArrow] (a/(a^2+b^2))\[Integral]x/(a+b Sinh[c+d x]) \…
100 Dist[b/(a^2+b^2),Int[x*(b-a*Sinh[c+d*x])/(a+b*Sinh[c+d*x])^2,x]] /;
484 (*Basis: Sinh[z]=E^z/2-E^-z/2*)
539 x*Sinh[a+b*x^n] -
604 (*Basis: Sinh[w+z]=Sinh[w] Cosh[z]+Cosh[w] Sinh[z]*)
629 Dist[Sinh[a],Int[Sinh[b*x^n]/x,x]] /;
1153 e*Sinh[a+b*x+c*x^2]/(2*c) /;
1678 Sinh[a*x*Log[b*x]^p]/a -
1804 …]Sinh[a/2+(b x)/2]^2 Sinh[a+b x]^n \[DifferentialD]x \[LongRightArrow] -(1/2)\[Integral]Sinh[a+b…
1812 Int[Sinh[c_.+d_.*x_]^2*Sinh[a_.+b_.*x_]^n_.,x_Symbol] :=
[all …]
/dports/math/reduce/Reduce-svn5758-src/packages/rubi_red/tests/SpecialFunctions/
H A DHyperbolicIntegralFunctions.m61 …Sinh[b*x]*SinhIntegral[b*x]/x^3, x, 16, b^2*CoshIntegral[2*b*x] - (b*Cosh[b*x]*Sinh[b*x])/(2*x) - …
65 {x*Sinh[b*x]*SinhIntegral[b*x], x, 10, CoshIntegral[2*b*x]/(2*b^2) - Log[x]/(2*b^2) - Sinh[b*x]^2/(…
66 …Sinh[b*x]*SinhIntegral[b*x], x, 12, -((5*x)/(4*b^2)) + (5*Cosh[b*x]*Sinh[b*x])/(4*b^3) - (x*Sinh[b…
67 …Sinh[b*x]*SinhIntegral[b*x], x, 19, -(x^2/b^2) + (3*CoshIntegral[2*b*x])/b^4 - (3*Log[x])/b^4 + (2…
85 {Sinh[a + b*x]*SinhIntegral[c + d*x]/x, x, 0, Int[(Sinh[a + b*x]*SinhIntegral[c + d*x])/x, x]}
164 …Sinh[b*x]*CoshIntegral[b*x]/x^3, x, 14, -(b/(4*x)) - (b*Cosh[2*b*x])/(2*x) + (1/2)*b^2*Int[(CoshIn…
165 {Sinh[b*x]*CoshIntegral[b*x]/x^2, x, 8, (1/2)*b*CoshIntegral[b*x]^2 + b*CoshIntegral[2*b*x] - (Cosh…
166 {Sinh[b*x]*CoshIntegral[b*x]/x, x, 0, Int[(CoshIntegral[b*x]*Sinh[b*x])/x, x]}
168 {x*Sinh[b*x]*CoshIntegral[b*x], x, 8, -(x/(2*b)) + (CoshIntegral[b*x]*(b*x*Cosh[b*x] - Sinh[b*x]))/…
169 …Sinh[b*x]*CoshIntegral[b*x], x, 14, -(x^2/(4*b)) + Cosh[b*x]^2/(4*b^3) - CoshIntegral[2*b*x]/b^3 -…
[all …]
/dports/math/reduce/Reduce-svn5758-src/contrib/rubi-red/rubi4/IntegrationProblems/MathematicaSyntaxFiles/SpecialFunctions/
H A DHyperbolicIntegralFunctions.m61 …Sinh[b*x]*SinhIntegral[b*x]/x^3, x, 16, b^2*CoshIntegral[2*b*x] - (b*Cosh[b*x]*Sinh[b*x])/(2*x) - …
65 {x*Sinh[b*x]*SinhIntegral[b*x], x, 10, CoshIntegral[2*b*x]/(2*b^2) - Log[x]/(2*b^2) - Sinh[b*x]^2/(…
66 …Sinh[b*x]*SinhIntegral[b*x], x, 12, -((5*x)/(4*b^2)) + (5*Cosh[b*x]*Sinh[b*x])/(4*b^3) - (x*Sinh[b…
67 …Sinh[b*x]*SinhIntegral[b*x], x, 19, -(x^2/b^2) + (3*CoshIntegral[2*b*x])/b^4 - (3*Log[x])/b^4 + (2…
85 {Sinh[a + b*x]*SinhIntegral[c + d*x]/x, x, 0, Int[(Sinh[a + b*x]*SinhIntegral[c + d*x])/x, x]}
164 …Sinh[b*x]*CoshIntegral[b*x]/x^3, x, 14, -(b/(4*x)) - (b*Cosh[2*b*x])/(2*x) + (1/2)*b^2*Int[(CoshIn…
165 {Sinh[b*x]*CoshIntegral[b*x]/x^2, x, 8, (1/2)*b*CoshIntegral[b*x]^2 + b*CoshIntegral[2*b*x] - (Cosh…
166 {Sinh[b*x]*CoshIntegral[b*x]/x, x, 0, Int[(CoshIntegral[b*x]*Sinh[b*x])/x, x]}
168 {x*Sinh[b*x]*CoshIntegral[b*x], x, 8, -(x/(2*b)) + (CoshIntegral[b*x]*(b*x*Cosh[b*x] - Sinh[b*x]))/…
169 …Sinh[b*x]*CoshIntegral[b*x], x, 14, -(x^2/(4*b)) + Cosh[b*x]^2/(4*b^3) - CoshIntegral[2*b*x]/b^3 -…
[all …]
/dports/math/reduce/Reduce-svn5758-src/packages/rubi_red/tests4/SpecialFunctions/
H A DHyperbolicIntegralFunctions.m67 …Sinh[b*x]*SinhIntegral[b*x]/x^3, x, 14, b^2*CoshIntegral[2*b*x] - (b*Cosh[b*x]*Sinh[b*x])/(2*x) - …
68 {Sinh[b*x]*SinhIntegral[b*x]/x^2, x, 5, b*Int[(Cosh[b*x]*SinhIntegral[b*x])/x, x] - Sinh[b*x]^2/x -…
71 {x*Sinh[b*x]*SinhIntegral[b*x], x, 8, CoshIntegral[2*b*x]/(2*b^2) - Log[x]/(2*b^2) - Sinh[b*x]^2/(2…
72 …Sinh[b*x]*SinhIntegral[b*x], x, 12, -((5*x)/(4*b^2)) + (5*Cosh[b*x]*Sinh[b*x])/(4*b^3) - (x*Sinh[b…
73 …Sinh[b*x]*SinhIntegral[b*x], x, 17, -(x^2/b^2) + (3*CoshIntegral[2*b*x])/b^4 - (3*Log[x])/b^4 + (2…
91 {Sinh[a + b*x]*SinhIntegral[c + d*x]/x, x, 0, Int[(Sinh[a + b*x]*SinhIntegral[c + d*x])/x, x]}
177 {Sinh[b*x]*CoshIntegral[b*x]/x^2, x, 7, (1/2)*b*CoshIntegral[b*x]^2 + b*CoshIntegral[2*b*x] - (Cosh…
178 {Sinh[b*x]*CoshIntegral[b*x]/x, x, 0, Int[(CoshIntegral[b*x]*Sinh[b*x])/x, x]}
180 {x*Sinh[b*x]*CoshIntegral[b*x], x, 8, -(x/(2*b)) + (x*Cosh[b*x]*CoshIntegral[b*x])/b - (Cosh[b*x]*S…
182 …Sinh[b*x]*CoshIntegral[b*x], x, 17, -((5*x)/(2*b^3)) - x^3/(6*b) + (x*Cosh[b*x]^2)/(2*b^3) + (6*x*…
[all …]
/dports/math/reduce/Reduce-svn5758-src/packages/rubi_red/rubi-rules/SpecialFunctions/
H A DHyperbolicIntegralFunctions.m31 (a+b*x)*CoshIntegral[a+b*x]/b - Sinh[a+b*x]/b /;
59 Dist[2,Int[Sinh[a+b*x]*SinhIntegral[a+b*x],x]] /;
254 Sinh[a+b*x]*CoshIntegral[c+d*x]/b -
294 x^m*Sinh[a+b*x]*CoshIntegral[c+d*x]/b -
324 Dist[d/(m+1),Int[x^(m+1)*Sinh[a+b*x]*Sinh[c+d*x]/(c+d*x),x]] -
355 (* ((Sinh[a+b x] SinhIntegral[c+d x])/b)-d/b \[Integral](Sinh[a+b x] Si…
364 Sinh[a+b*x]*SinhIntegral[c+d*x]/b -
365 Dist[d/b,Int[Sinh[a+b*x]*Sinh[c+d*x]/(c+d*x),x]] /;
394 (* d/b \[Integral](x^m Sinh[a+b x] Sinh[c+d x])/(c+d x) \[DifferentialD]x-m/b \[Integral…
403 x^m*Sinh[a+b*x]*SinhIntegral[c+d*x]/b -
[all …]

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