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Searched refs:Tanh (Results 1 – 25 of 1266) sorted by relevance

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/dports/math/reduce/Reduce-svn5758-src/contrib/rubi-red/mathematicatests/
H A DHyperbolicTangentFunctions.m13 {Tanh[a+b*x]^2, x, 1, x - Tanh[a+b*x]/b}
15 {Tanh[a+b*x]^4, x, 2, x - Tanh[a + b*x]/b - Tanh[a + b*x]^3/(3*b)}
68 {Sqrt[a*Tanh[x]^3], x, 8, ((ArcTan[Sqrt[Tanh[x]]] + ArcTanh[Sqrt[Tanh[x]]] - 2*Sqrt[Tanh[x]])*Sqrt[…
73 …(a*Tanh[x]^3)^(3/2),x, 9, -((a*Sqrt[a*Tanh[x]^3]*(21*ArcTan[Sqrt[Tanh[x]]] - 21*ArcTanh[Sqrt[Tanh[…
74 …Tanh[x]^4)^(3/2),x, 4, (-a)*Coth[x]*Sqrt[a*Tanh[x]^4] + a*x*Coth[x]^2*Sqrt[a*Tanh[x]^4] - (1/3)*a*…
78 {1/Sqrt[a*Tanh[x]^3], x, 10, -(((2 + (ArcTan[Sqrt[Tanh[x]]] - ArcTanh[Sqrt[Tanh[x]]])*Sqrt[Tanh[x]]…
79 {1/Sqrt[a*Tanh[x]^4], x, 2, -(Tanh[x]/Sqrt[a*Tanh[x]^4]) + (x*Tanh[x]^2)/Sqrt[a*Tanh[x]^4]}
91 {1/(1 + Tanh[x])^3, x, 3, x/8 - 1/(6*(1 + Tanh[x])^3) - 1/(8*(1 + Tanh[x])^2) - 1/(8*(1 + Tanh[x]))}
130 {Sqrt[-1 - Tanh[x]^2], x, 4, ArcTan[Tanh[x]/Sqrt[-1 - Tanh[x]^2]] - Sqrt[2]*ArcTan[(Sqrt[2]*Tanh[x]…
139 {(1 + Tanh[x]^2)^(3/2), x, 8, (-(5/2))*ArcSinh[Tanh[x]] + 2*Sqrt[2]*ArcTanh[(Sqrt[2]*Tanh[x])/Sqrt[…
[all …]
H A DHyperbolicSecantFunctions.m15 {Sech[a+b*x]^4, x, 2, Tanh[a + b*x]/b - Tanh[a + b*x]^3/(3*b)}
18 {Sech[7*x]^4, x, 2, (1/7)*Tanh[7*x] - (1/21)*Tanh[7*x]^3}
19 {Sech[Pi*x]^6, x, 3, Tanh[Pi*x]/Pi - (2*Tanh[Pi*x]^3)/(3*Pi) + Tanh[Pi*x]^5/(5*Pi)}
100 …Sech[x]^4]*Sinh[x]*(3003 - 6006*Tanh[x]^2 + 9009*Tanh[x]^4 - 8580*Tanh[x]^6 + 5005*Tanh[x]^8 - 163…
101 …)*a^2*Cosh[x]*Sqrt[a*Sech[x]^4]*Sinh[x]*(315 - 420*Tanh[x]^2 + 378*Tanh[x]^4 - 180*Tanh[x]^6 + 35*…
147 {(a + b*Sech[x]^2)^2, x, 5, a^2*x + 2*a*b*Tanh[x] + b^2*Tanh[x] - (1/3)*b^2*Tanh[x]^3}
148 …2)^3, x, 8, a^3*x + 3*a^2*b*Tanh[x] + 3*a*b^2*Tanh[x] + b^3*Tanh[x] - a*b^2*Tanh[x]^3 - (2/3)*b^3*…
156 {Sqrt[1 + Sech[x]^2], x, 4, ArcSin[Tanh[x]/Sqrt[2]] + ArcTanh[Tanh[x]/Sqrt[2 - Tanh[x]^2]]}
159 {Sqrt[-1 - Sech[x]^2], x, 4, -ArcTan[Tanh[x]/Sqrt[-2 + Tanh[x]^2]] - ArcTanh[Tanh[x]/Sqrt[-2 + Tanh…
168 … Sech[x]^2)^(3/2), x, 7, 2*ArcSin[Tanh[x]/Sqrt[2]] + ArcTanh[Tanh[x]/Sqrt[2 - Tanh[x]^2]] + (1/2)*…
[all …]
H A DHyperbolicFunctions.m167 …Tanh[x]^5/Sqrt[a + b*Tanh[x]^2 + c*Tanh[x]^4], x, 9, (b*ArcTanh[(b + 2*c*Tanh[x]^2)/(2*Sqrt[c]*Sqr…
168 …Tanh[x]^3/Sqrt[a + b*Tanh[x]^2 + c*Tanh[x]^4], x, 7, -(ArcTanh[(b + 2*c*Tanh[x]^2)/(2*Sqrt[c]*Sqrt…
169 {Tanh[x]/Sqrt[a + b*Tanh[x]^2 + c*Tanh[x]^4], x, 4, ArcTanh[(2*a + b + (b + 2*c)*Tanh[x]^2)/(2*Sqrt…
171 …Tanh[x]^2 + c*Tanh[x]^4], x, 9, -(ArcTanh[(2*a + b*Tanh[x]^2)/(2*Sqrt[a]*Sqrt[a + b*Tanh[x]^2 + c*…
181 (* {Tanh[x]^5*Sqrt[a + b*Tanh[x]^2 + c*Tanh[x]^4], x, 0, 0} *)
182 (* {Tanh[x]^3*Sqrt[a + b*Tanh[x]^2 + c*Tanh[x]^4], x, 0, 0} *)
183 …Tanh[x]*Sqrt[a + b*Tanh[x]^2 + c*Tanh[x]^4], x, 6, -(((b + 2*c)*ArcTanh[(b + 2*c*Tanh[x]^2)/(2*Sqr…
435 {Sech[x]^2*(2 - Tanh[x]^2)/(1 - Tanh[x]^2), x, -4, x + Tanh[x]}
443 {Sech[x]^2*Sqrt[1 + Tanh[x]^2], x, 3, (1/2)*ArcSinh[Tanh[x]] + (1/2)*Tanh[x]*Sqrt[1 + Tanh[x]^2]}
446 {Sech[x]^2/(2 + 2*Tanh[x] + Tanh[x]^2), x, 2, ArcTan[1 + Tanh[x]]}
[all …]
H A DTwoHyperbolicFunctions.m129 {Sech[x]^8*Tanh[x]^6, x, 3, Tanh[x]^7/7 - Tanh[x]^9/3 + (3*Tanh[x]^11)/11 - Tanh[x]^13/13}
771 {Tanh[x]/(1 + Tanh[x]), x, 2, x/2 + 1/(2*(1 + Tanh[x]))}
773 {Tanh[x]^3/(1 + Tanh[x]), x, 5, (3*x)/2 - Log[Cosh[x]] - Tanh[x] + 1/(2*(1 + Tanh[x]))}
774 {Tanh[x]^4/(1 + Tanh[x]), x, 7, -((3*x)/2) + 2*Log[Cosh[x]] + Tanh[x] - Tanh[x]^2/2 - 1/(2*(1 + Tan…
798 {Sech[x]^4/(1 + Tanh[x]), x, 2, Tanh[x] - Tanh[x]^2/2}
853 {Tanh[x]^4/(1 + Coth[x]), x, 9, (5*x)/2 - 2*Log[Cosh[x]] - 2*Tanh[x] + Tanh[x]^2/2 - Tanh[x]^3/3 + …
1306 {Tanh[x]*(1 + Tanh[x])^(3/2), x, 3, 2*Sqrt[2]*ArcTanh[Sqrt[1 + Tanh[x]]/Sqrt[2]] - 2*Sqrt[1 + Tanh[…
1313 {Tanh[x]^2/Sqrt[1 + Tanh[x]], x, 6, ArcTanh[Sqrt[1 + Tanh[x]]/Sqrt[2]]/Sqrt[2] - 1/Sqrt[1 + Tanh[x]…
1386 …Tanh[x]^2*(a + b*Tanh[x]^2)^(3/2), x, 13, -((3*a^2*ArcTanh[(Sqrt[b]*Tanh[x])/Sqrt[a + b*Tanh[x]^2]…
1394 {Tanh[x]^2/(a + b*Tanh[x]^2)^(3/2), x, 7, ArcTanh[(Sqrt[a + b]*Tanh[x])/Sqrt[a + b*Tanh[x]^2]]/(a +…
[all …]
/dports/math/reduce/Reduce-svn5758-src/packages/rubi_red/tests/HyperbolicFunctions/
H A DHyperbolicTangentFunctions.m13 {Tanh[a+b*x]^2, x, 1, x - Tanh[a+b*x]/b}
15 {Tanh[a+b*x]^4, x, 2, x - Tanh[a + b*x]/b - Tanh[a + b*x]^3/(3*b)}
68 {Sqrt[a*Tanh[x]^3], x, 8, ((ArcTan[Sqrt[Tanh[x]]] + ArcTanh[Sqrt[Tanh[x]]] - 2*Sqrt[Tanh[x]])*Sqrt[…
73 …(a*Tanh[x]^3)^(3/2),x, 9, -((a*Sqrt[a*Tanh[x]^3]*(21*ArcTan[Sqrt[Tanh[x]]] - 21*ArcTanh[Sqrt[Tanh[…
74 …Tanh[x]^4)^(3/2),x, 4, (-a)*Coth[x]*Sqrt[a*Tanh[x]^4] + a*x*Coth[x]^2*Sqrt[a*Tanh[x]^4] - (1/3)*a*…
78 {1/Sqrt[a*Tanh[x]^3], x, 10, -(((2 + (ArcTan[Sqrt[Tanh[x]]] - ArcTanh[Sqrt[Tanh[x]]])*Sqrt[Tanh[x]]…
79 {1/Sqrt[a*Tanh[x]^4], x, 2, -(Tanh[x]/Sqrt[a*Tanh[x]^4]) + (x*Tanh[x]^2)/Sqrt[a*Tanh[x]^4]}
91 {1/(1 + Tanh[x])^3, x, 3, x/8 - 1/(6*(1 + Tanh[x])^3) - 1/(8*(1 + Tanh[x])^2) - 1/(8*(1 + Tanh[x]))}
130 {Sqrt[-1 - Tanh[x]^2], x, 4, ArcTan[Tanh[x]/Sqrt[-1 - Tanh[x]^2]] - Sqrt[2]*ArcTan[(Sqrt[2]*Tanh[x]…
139 {(1 + Tanh[x]^2)^(3/2), x, 8, (-(5/2))*ArcSinh[Tanh[x]] + 2*Sqrt[2]*ArcTanh[(Sqrt[2]*Tanh[x])/Sqrt[…
[all …]
H A DHyperbolicSecantFunctions.m15 {Sech[a+b*x]^4, x, 2, Tanh[a + b*x]/b - Tanh[a + b*x]^3/(3*b)}
18 {Sech[7*x]^4, x, 2, (1/7)*Tanh[7*x] - (1/21)*Tanh[7*x]^3}
19 {Sech[Pi*x]^6, x, 3, Tanh[Pi*x]/Pi - (2*Tanh[Pi*x]^3)/(3*Pi) + Tanh[Pi*x]^5/(5*Pi)}
100 …Sech[x]^4]*Sinh[x]*(3003 - 6006*Tanh[x]^2 + 9009*Tanh[x]^4 - 8580*Tanh[x]^6 + 5005*Tanh[x]^8 - 163…
101 …)*a^2*Cosh[x]*Sqrt[a*Sech[x]^4]*Sinh[x]*(315 - 420*Tanh[x]^2 + 378*Tanh[x]^4 - 180*Tanh[x]^6 + 35*…
147 {(a + b*Sech[x]^2)^2, x, 5, a^2*x + 2*a*b*Tanh[x] + b^2*Tanh[x] - (1/3)*b^2*Tanh[x]^3}
148 …2)^3, x, 8, a^3*x + 3*a^2*b*Tanh[x] + 3*a*b^2*Tanh[x] + b^3*Tanh[x] - a*b^2*Tanh[x]^3 - (2/3)*b^3*…
156 {Sqrt[1 + Sech[x]^2], x, 4, ArcSin[Tanh[x]/Sqrt[2]] + ArcTanh[Tanh[x]/Sqrt[2 - Tanh[x]^2]]}
159 {Sqrt[-1 - Sech[x]^2], x, 4, -ArcTan[Tanh[x]/Sqrt[-2 + Tanh[x]^2]] - ArcTanh[Tanh[x]/Sqrt[-2 + Tanh…
168 … Sech[x]^2)^(3/2), x, 7, 2*ArcSin[Tanh[x]/Sqrt[2]] + ArcTanh[Tanh[x]/Sqrt[2 - Tanh[x]^2]] + (1/2)*…
[all …]
H A DHyperbolicFunctions.m167 …Tanh[x]^5/Sqrt[a + b*Tanh[x]^2 + c*Tanh[x]^4], x, 9, (b*ArcTanh[(b + 2*c*Tanh[x]^2)/(2*Sqrt[c]*Sqr…
168 …Tanh[x]^3/Sqrt[a + b*Tanh[x]^2 + c*Tanh[x]^4], x, 7, -(ArcTanh[(b + 2*c*Tanh[x]^2)/(2*Sqrt[c]*Sqrt…
169 {Tanh[x]/Sqrt[a + b*Tanh[x]^2 + c*Tanh[x]^4], x, 4, ArcTanh[(2*a + b + (b + 2*c)*Tanh[x]^2)/(2*Sqrt…
171 …Tanh[x]^2 + c*Tanh[x]^4], x, 9, -(ArcTanh[(2*a + b*Tanh[x]^2)/(2*Sqrt[a]*Sqrt[a + b*Tanh[x]^2 + c*…
181 (* {Tanh[x]^5*Sqrt[a + b*Tanh[x]^2 + c*Tanh[x]^4], x, 0, 0} *)
182 (* {Tanh[x]^3*Sqrt[a + b*Tanh[x]^2 + c*Tanh[x]^4], x, 0, 0} *)
183 …Tanh[x]*Sqrt[a + b*Tanh[x]^2 + c*Tanh[x]^4], x, 6, -(((b + 2*c)*ArcTanh[(b + 2*c*Tanh[x]^2)/(2*Sqr…
435 {Sech[x]^2*(2 - Tanh[x]^2)/(1 - Tanh[x]^2), x, -4, x + Tanh[x]}
443 {Sech[x]^2*Sqrt[1 + Tanh[x]^2], x, 3, (1/2)*ArcSinh[Tanh[x]] + (1/2)*Tanh[x]*Sqrt[1 + Tanh[x]^2]}
446 {Sech[x]^2/(2 + 2*Tanh[x] + Tanh[x]^2), x, 2, ArcTan[1 + Tanh[x]]}
[all …]
H A DTwoHyperbolicFunctions.m129 {Sech[x]^8*Tanh[x]^6, x, 3, Tanh[x]^7/7 - Tanh[x]^9/3 + (3*Tanh[x]^11)/11 - Tanh[x]^13/13}
771 {Tanh[x]/(1 + Tanh[x]), x, 2, x/2 + 1/(2*(1 + Tanh[x]))}
773 {Tanh[x]^3/(1 + Tanh[x]), x, 5, (3*x)/2 - Log[Cosh[x]] - Tanh[x] + 1/(2*(1 + Tanh[x]))}
774 {Tanh[x]^4/(1 + Tanh[x]), x, 7, -((3*x)/2) + 2*Log[Cosh[x]] + Tanh[x] - Tanh[x]^2/2 - 1/(2*(1 + Tan…
798 {Sech[x]^4/(1 + Tanh[x]), x, 2, Tanh[x] - Tanh[x]^2/2}
853 {Tanh[x]^4/(1 + Coth[x]), x, 9, (5*x)/2 - 2*Log[Cosh[x]] - 2*Tanh[x] + Tanh[x]^2/2 - Tanh[x]^3/3 + …
1306 {Tanh[x]*(1 + Tanh[x])^(3/2), x, 3, 2*Sqrt[2]*ArcTanh[Sqrt[1 + Tanh[x]]/Sqrt[2]] - 2*Sqrt[1 + Tanh[…
1313 {Tanh[x]^2/Sqrt[1 + Tanh[x]], x, 6, ArcTanh[Sqrt[1 + Tanh[x]]/Sqrt[2]]/Sqrt[2] - 1/Sqrt[1 + Tanh[x]…
1386 …Tanh[x]^2*(a + b*Tanh[x]^2)^(3/2), x, 13, -((3*a^2*ArcTanh[(Sqrt[b]*Tanh[x])/Sqrt[a + b*Tanh[x]^2]…
1394 {Tanh[x]^2/(a + b*Tanh[x]^2)^(3/2), x, 7, ArcTanh[(Sqrt[a + b]*Tanh[x])/Sqrt[a + b*Tanh[x]^2]]/(a +…
[all …]
/dports/math/reduce/Reduce-svn5758-src/contrib/rubi-red/rubi4/IntegrationProblems/MathematicaSyntaxFiles/HyperbolicFunctions/
H A DHyperbolicTangentFunctions.m13 {Tanh[a+b*x]^2, x, 1, x - Tanh[a+b*x]/b}
15 {Tanh[a+b*x]^4, x, 2, x - Tanh[a + b*x]/b - Tanh[a + b*x]^3/(3*b)}
68 {Sqrt[a*Tanh[x]^3], x, 8, ((ArcTan[Sqrt[Tanh[x]]] + ArcTanh[Sqrt[Tanh[x]]] - 2*Sqrt[Tanh[x]])*Sqrt[…
73 …(a*Tanh[x]^3)^(3/2),x, 9, -((a*Sqrt[a*Tanh[x]^3]*(21*ArcTan[Sqrt[Tanh[x]]] - 21*ArcTanh[Sqrt[Tanh[…
74 …Tanh[x]^4)^(3/2),x, 4, (-a)*Coth[x]*Sqrt[a*Tanh[x]^4] + a*x*Coth[x]^2*Sqrt[a*Tanh[x]^4] - (1/3)*a*…
78 {1/Sqrt[a*Tanh[x]^3], x, 10, -(((2 + (ArcTan[Sqrt[Tanh[x]]] - ArcTanh[Sqrt[Tanh[x]]])*Sqrt[Tanh[x]]…
79 {1/Sqrt[a*Tanh[x]^4], x, 2, -(Tanh[x]/Sqrt[a*Tanh[x]^4]) + (x*Tanh[x]^2)/Sqrt[a*Tanh[x]^4]}
91 {1/(1 + Tanh[x])^3, x, 3, x/8 - 1/(6*(1 + Tanh[x])^3) - 1/(8*(1 + Tanh[x])^2) - 1/(8*(1 + Tanh[x]))}
130 {Sqrt[-1 - Tanh[x]^2], x, 4, ArcTan[Tanh[x]/Sqrt[-1 - Tanh[x]^2]] - Sqrt[2]*ArcTan[(Sqrt[2]*Tanh[x]…
139 {(1 + Tanh[x]^2)^(3/2), x, 8, (-(5/2))*ArcSinh[Tanh[x]] + 2*Sqrt[2]*ArcTanh[(Sqrt[2]*Tanh[x])/Sqrt[…
[all …]
H A DHyperbolicSecantFunctions.m15 {Sech[a+b*x]^4, x, 2, Tanh[a + b*x]/b - Tanh[a + b*x]^3/(3*b)}
18 {Sech[7*x]^4, x, 2, (1/7)*Tanh[7*x] - (1/21)*Tanh[7*x]^3}
19 {Sech[Pi*x]^6, x, 3, Tanh[Pi*x]/Pi - (2*Tanh[Pi*x]^3)/(3*Pi) + Tanh[Pi*x]^5/(5*Pi)}
100 …Sech[x]^4]*Sinh[x]*(3003 - 6006*Tanh[x]^2 + 9009*Tanh[x]^4 - 8580*Tanh[x]^6 + 5005*Tanh[x]^8 - 163…
101 …)*a^2*Cosh[x]*Sqrt[a*Sech[x]^4]*Sinh[x]*(315 - 420*Tanh[x]^2 + 378*Tanh[x]^4 - 180*Tanh[x]^6 + 35*…
147 {(a + b*Sech[x]^2)^2, x, 5, a^2*x + 2*a*b*Tanh[x] + b^2*Tanh[x] - (1/3)*b^2*Tanh[x]^3}
148 …2)^3, x, 8, a^3*x + 3*a^2*b*Tanh[x] + 3*a*b^2*Tanh[x] + b^3*Tanh[x] - a*b^2*Tanh[x]^3 - (2/3)*b^3*…
156 {Sqrt[1 + Sech[x]^2], x, 4, ArcSin[Tanh[x]/Sqrt[2]] + ArcTanh[Tanh[x]/Sqrt[2 - Tanh[x]^2]]}
159 {Sqrt[-1 - Sech[x]^2], x, 4, -ArcTan[Tanh[x]/Sqrt[-2 + Tanh[x]^2]] - ArcTanh[Tanh[x]/Sqrt[-2 + Tanh…
168 … Sech[x]^2)^(3/2), x, 7, 2*ArcSin[Tanh[x]/Sqrt[2]] + ArcTanh[Tanh[x]/Sqrt[2 - Tanh[x]^2]] + (1/2)*…
[all …]
H A DHyperbolicFunctions.m167 …Tanh[x]^5/Sqrt[a + b*Tanh[x]^2 + c*Tanh[x]^4], x, 9, (b*ArcTanh[(b + 2*c*Tanh[x]^2)/(2*Sqrt[c]*Sqr…
168 …Tanh[x]^3/Sqrt[a + b*Tanh[x]^2 + c*Tanh[x]^4], x, 7, -(ArcTanh[(b + 2*c*Tanh[x]^2)/(2*Sqrt[c]*Sqrt…
169 {Tanh[x]/Sqrt[a + b*Tanh[x]^2 + c*Tanh[x]^4], x, 4, ArcTanh[(2*a + b + (b + 2*c)*Tanh[x]^2)/(2*Sqrt…
171 …Tanh[x]^2 + c*Tanh[x]^4], x, 9, -(ArcTanh[(2*a + b*Tanh[x]^2)/(2*Sqrt[a]*Sqrt[a + b*Tanh[x]^2 + c*…
181 (* {Tanh[x]^5*Sqrt[a + b*Tanh[x]^2 + c*Tanh[x]^4], x, 0, 0} *)
182 (* {Tanh[x]^3*Sqrt[a + b*Tanh[x]^2 + c*Tanh[x]^4], x, 0, 0} *)
183 …Tanh[x]*Sqrt[a + b*Tanh[x]^2 + c*Tanh[x]^4], x, 6, -(((b + 2*c)*ArcTanh[(b + 2*c*Tanh[x]^2)/(2*Sqr…
435 {Sech[x]^2*(2 - Tanh[x]^2)/(1 - Tanh[x]^2), x, -4, x + Tanh[x]}
443 {Sech[x]^2*Sqrt[1 + Tanh[x]^2], x, 3, (1/2)*ArcSinh[Tanh[x]] + (1/2)*Tanh[x]*Sqrt[1 + Tanh[x]^2]}
446 {Sech[x]^2/(2 + 2*Tanh[x] + Tanh[x]^2), x, 2, ArcTan[1 + Tanh[x]]}
[all …]
H A DTwoHyperbolicFunctions.m129 {Sech[x]^8*Tanh[x]^6, x, 3, Tanh[x]^7/7 - Tanh[x]^9/3 + (3*Tanh[x]^11)/11 - Tanh[x]^13/13}
771 {Tanh[x]/(1 + Tanh[x]), x, 2, x/2 + 1/(2*(1 + Tanh[x]))}
773 {Tanh[x]^3/(1 + Tanh[x]), x, 5, (3*x)/2 - Log[Cosh[x]] - Tanh[x] + 1/(2*(1 + Tanh[x]))}
774 {Tanh[x]^4/(1 + Tanh[x]), x, 7, -((3*x)/2) + 2*Log[Cosh[x]] + Tanh[x] - Tanh[x]^2/2 - 1/(2*(1 + Tan…
798 {Sech[x]^4/(1 + Tanh[x]), x, 2, Tanh[x] - Tanh[x]^2/2}
853 {Tanh[x]^4/(1 + Coth[x]), x, 9, (5*x)/2 - 2*Log[Cosh[x]] - 2*Tanh[x] + Tanh[x]^2/2 - Tanh[x]^3/3 + …
1306 {Tanh[x]*(1 + Tanh[x])^(3/2), x, 3, 2*Sqrt[2]*ArcTanh[Sqrt[1 + Tanh[x]]/Sqrt[2]] - 2*Sqrt[1 + Tanh[…
1313 {Tanh[x]^2/Sqrt[1 + Tanh[x]], x, 6, ArcTanh[Sqrt[1 + Tanh[x]]/Sqrt[2]]/Sqrt[2] - 1/Sqrt[1 + Tanh[x]…
1386 …Tanh[x]^2*(a + b*Tanh[x]^2)^(3/2), x, 13, -((3*a^2*ArcTanh[(Sqrt[b]*Tanh[x])/Sqrt[a + b*Tanh[x]^2]…
1394 {Tanh[x]^2/(a + b*Tanh[x]^2)^(3/2), x, 7, ArcTanh[(Sqrt[a + b]*Tanh[x])/Sqrt[a + b*Tanh[x]^2]]/(a +…
[all …]
/dports/math/reduce/Reduce-svn5758-src/packages/rubi_red/tests4/HyperbolicFunctions/
H A DHyperbolicTangentFunctions.m22 {Tanh[a + b*x]^6, x, 4, x - Tanh[a + b*x]/b - Tanh[a + b*x]^3/(3*b) - Tanh[a + b*x]^5/(5*b)}
87 …t[Tanh[x]^3], x, 6, -2*Coth[x]*Sqrt[Tanh[x]^3] + (ArcTan[Sqrt[Tanh[x]]]*Sqrt[Tanh[x]^3])/Tanh[x]^(…
90 …Tanh[x]^3)^(3/2),x, 7, (-(2/3))*a*Sqrt[a*Tanh[x]^3] - (a*ArcTan[Sqrt[Tanh[x]]]*Sqrt[a*Tanh[x]^3])/…
91 …Tanh[x]^3], x, 6, -2*Coth[x]*Sqrt[a*Tanh[x]^3] + (ArcTan[Sqrt[Tanh[x]]]*Sqrt[a*Tanh[x]^3])/Tanh[x]…
92 …Tanh[x]^3], x, 6, -((2*Tanh[x])/Sqrt[a*Tanh[x]^3]) - (ArcTan[Sqrt[Tanh[x]]]*Tanh[x]^(3/2))/Sqrt[a*…
99 …Tanh[x]^4)^(3/2),x, 5, (-a)*Coth[x]*Sqrt[a*Tanh[x]^4] + a*x*Coth[x]^2*Sqrt[a*Tanh[x]^4] - (1/3)*a*…
101 {1/Sqrt[a*Tanh[x]^4], x, 3, -(Tanh[x]/Sqrt[a*Tanh[x]^4]) + (x*Tanh[x]^2)/Sqrt[a*Tanh[x]^4]}
170 {Sech[x]^6/(1 + Tanh[x]), x, 4, Tanh[x] - Tanh[x]^2/2 - Tanh[x]^3/3 + Tanh[x]^4/4}
199 {Tanh[x]^5/(1 + Tanh[x]), x, 6, (5*x)/2 - 2*Log[Cosh[x]] - (5*Tanh[x])/2 + Tanh[x]^2 - (5*Tanh[x]^3…
200 {Tanh[x]^4/(1 + Tanh[x]), x, 5, -((3*x)/2) + 2*Log[Cosh[x]] + (3*Tanh[x])/2 - Tanh[x]^2 + Tanh[x]^3…
[all …]
H A Dtanh^3.m259 …Tanh[x]^4*Sqrt[a + b*Tanh[x]^3], x, 6, ((a^2 - 4*a*b - 8*b^2)*ArcTanh[(Sqrt[b]*Tanh[x])/Sqrt[a + b…
261 …Tanh[x]^2*Sqrt[a + b*Tanh[x]^3], x, 5, -(((a + 2*b)*ArcTanh[(Sqrt[b]*Tanh[x])/Sqrt[a + b*Tanh[x]^3…
272 …Tanh[x]^2*(a + b*Tanh[x]^3)^(3/2), x, 6, -(((3*a^2 + 12*a*b + 8*b^2)*ArcTanh[(Sqrt[b]*Tanh[x])/Sqr…
284 …Tanh[x]^4/Sqrt[a + b*Tanh[x]^3], x, 5, ((a - 2*b)*ArcTanh[(Sqrt[b]*Tanh[x])/Sqrt[a + b*Tanh[x]^3]]…
295 …Tanh[x]^4/(a + b*Tanh[x]^3)^(3/2), x, 5, -(ArcTanh[(Sqrt[b]*Tanh[x])/Sqrt[a + b*Tanh[x]^3]]/b^(3/2…
297 {Tanh[x]^2/(a + b*Tanh[x]^3)^(3/2), x, 3, ArcTanh[(Sqrt[a + b]*Tanh[x])/Sqrt[a + b*Tanh[x]^3]]/(a +…
299 {Tanh[x]^0/(a + b*Tanh[x]^3)^(3/2), x, 3, ArcTanh[(Sqrt[a + b]*Tanh[x])/Sqrt[a + b*Tanh[x]^3]]/(a +…
304 …Tanh[x]^6/(a + b*Tanh[x]^3)^(5/2), x, 6, -(ArcTanh[(Sqrt[b]*Tanh[x])/Sqrt[a + b*Tanh[x]^3]]/b^(5/2…
306 …Tanh[x]^4/(a + b*Tanh[x]^3)^(5/2), x, 5, ArcTanh[(Sqrt[a + b]*Tanh[x])/Sqrt[a + b*Tanh[x]^3]]/(a +…
308 …Tanh[x]^2/(a + b*Tanh[x]^3)^(5/2), x, 5, ArcTanh[(Sqrt[a + b]*Tanh[x])/Sqrt[a + b*Tanh[x]^3]]/(a +…
[all …]
H A DHyperbolicSecantFunctions.m20 {Sech[a + b*x]^6, x, 2, Tanh[a + b*x]/b - (2*Tanh[a + b*x]^3)/(3*b) + Tanh[a + b*x]^5/(5*b)}
26 {Sech[Pi*x]^6, x, 2, Tanh[Pi*x]/Pi - (2*Tanh[Pi*x]^3)/(3*Pi) + Tanh[Pi*x]^5/(5*Pi)}
70 …, 4, Tanh[a + b*x]/(5*b*(1 - Tanh[a + b*x]^2)^(5/2)) + (4*Tanh[a + b*x])/(15*b*(1 - Tanh[a + b*x]^…
71 …Tanh[a + b*x]/(7*b*(1 - Tanh[a + b*x]^2)^(7/2)) + (6*Tanh[a + b*x])/(35*b*(1 - Tanh[a + b*x]^2)^(5…
220 {Tanh[x]^6/(a + a*Sech[x]), x, 7, x/a - (3*ArcTan[Sinh[x]])/(8*a) - Tanh[x]/a + (3*Sech[x]*Tanh[x])…
547 {Tanh[x]^2/(a + b*Sech[x]^2)^(3/2), x, 3, ArcTanh[(Sqrt[a]*Tanh[x])/Sqrt[a + b - b*Tanh[x]^2]]/a^(3…
554 …Tanh[x]^6/(a + b*Sech[x]^2)^(5/2), x, 6, -(ArcTan[(Sqrt[b]*Tanh[x])/Sqrt[a + b - b*Tanh[x]^2]]/b^(…
558 …Tanh[x]^2/(a + b*Sech[x]^2)^(5/2), x, 5, ArcTanh[(Sqrt[a]*Tanh[x])/Sqrt[a + b - b*Tanh[x]^2]]/a^(5…
572 … Sech[x]^2)^(3/2), x, 5, 2*ArcSin[Tanh[x]/Sqrt[2]] + ArcTanh[Tanh[x]/Sqrt[2 - Tanh[x]^2]] + (1/2)*…
587 …]^2)^(3/2), x, 5, ArcTan[Tanh[x]/Sqrt[-2 + Tanh[x]^2]] + 2*ArcTanh[Tanh[x]/Sqrt[-2 + Tanh[x]^2]] -…
[all …]
H A DHyperbolicFunctions.m152 …Tanh[x]^5/Sqrt[a + b*Tanh[x]^2 + c*Tanh[x]^4], x, 9, (b*ArcTanh[(b + 2*c*Tanh[x]^2)/(2*Sqrt[c]*Sqr…
153 …Tanh[x]^3/Sqrt[a + b*Tanh[x]^2 + c*Tanh[x]^4], x, 6, -(ArcTanh[(b + 2*c*Tanh[x]^2)/(2*Sqrt[c]*Sqrt…
154 {Tanh[x]/Sqrt[a + b*Tanh[x]^2 + c*Tanh[x]^4], x, 4, ArcTanh[(2*a + b + (b + 2*c)*Tanh[x]^2)/(2*Sqrt…
166 (* {Tanh[x]^5*Sqrt[a + b*Tanh[x]^2 + c*Tanh[x]^4], x, 0, 0} *)
167 (* {Tanh[x]^3*Sqrt[a + b*Tanh[x]^2 + c*Tanh[x]^4], x, 0, 0} *)
168 …Tanh[x]*Sqrt[a + b*Tanh[x]^2 + c*Tanh[x]^4], x, 7, -(((b + 2*c)*ArcTanh[(b + 2*c*Tanh[x]^2)/(2*Sqr…
418 {Sech[x]^2*(2 - Tanh[x]^2)/(1 - Tanh[x]^2), x, 4, x + Tanh[x]}
426 {Sech[x]^2*Sqrt[1 + Tanh[x]^2], x, 3, (1/2)*ArcSinh[Tanh[x]] + (1/2)*Tanh[x]*Sqrt[1 + Tanh[x]^2]}
427 {Sech[x]^2/(Tanh[x]^2 + Tanh[x]^3), x, 3, -Coth[x] - Log[Tanh[x]] + Log[1 + Tanh[x]]}
428 {Sech[x]^2/(-Tanh[x]^2 + Tanh[x]^3), x, 3, Coth[x] + Log[1 - Tanh[x]] - Log[Tanh[x]]}
[all …]
H A DHyperbolicCosineFunctions.m62 …),x, 4, (8/15)*a^2*Sqrt[a*Cosh[x]^2]*Tanh[x] + (4/15)*a*(a*Cosh[x]^2)^(3/2)*Tanh[x] + (1/5)*(a*Cos…
188 …((3*ArcTan[Sinh[x]])/(2*a)) + (4*Tanh[x])/a - (3*Sech[x]*Tanh[x])/(2*a) - (Sech[x]^2*Tanh[x])/(a +…
262 …Tanh[x]^4/(a + b*Cosh[x]), x, 6, (b*ArcTan[Sinh[x]])/(2*a^2) + (b*(a^2 - b^2)*ArcTan[Sinh[x]])/a^4…
272 {Tanh[x]^6/(a + a*Cosh[x]), x, 4, (3*ArcTan[Sinh[x]])/(8*a) - (3*Sech[x]*Tanh[x])/(8*a) - (Sech[x]*…
274 {Tanh[x]^4/(a + a*Cosh[x]), x, 3, ArcTan[Sinh[x]]/(2*a) - (Sech[x]*Tanh[x])/(2*a) - Tanh[x]^3/(3*a)}
276 {Tanh[x]^2/(a + a*Cosh[x]), x, 2, ArcTan[Sinh[x]]/a - Tanh[x]/a}
320 …)*ArcTanh[(Sqrt[a]*Tanh[x])/Sqrt[a + b]])/(b^3*Sqrt[a + b]) + Tanh[x]/(4*b*(1 - Tanh[x]^2)^2) - ((…
322 …Tanh[x])/Sqrt[a + b]])/(b^4*Sqrt[a + b]) + Tanh[x]/(6*b*(1 - Tanh[x]^2)^3) - ((6*a - 5*b)*Tanh[x])…
327 …Tanh[x])/Sqrt[a + b]])/(8*a^(5/2)*(a + b)^(5/2)) - (b*Tanh[x]*(1 - Tanh[x]^2))/(4*a*(a + b)*(a + b…
330 {1/(1 + Cosh[x]^2)^2, x, 3, (3*ArcTanh[Tanh[x]/Sqrt[2]])/(4*Sqrt[2]) - Tanh[x]/(4*(2 - Tanh[x]^2))}
[all …]
/dports/math/reduce/Reduce-svn5758-src/packages/rubi_red/rubi-rules/HyperbolicFunctions/
H A DHyperbolicTangentFunctions.m77 x - Tanh[a+b*x]/b /;
104 (*Basis: Tanh[z]^n=(Tanh[z]^(n-1) Sinh[z])/Cosh[z]*)
373 (*\[Integral](A+B Tanh[c+d x])(a+b Tanh[c+d x])^n \[DifferentialD]x*)
397 Int[(A_.+B_.*Tanh[c_.+d_.*x_])/(a_.+b_.*Tanh[c_.+d_.*x_]),x_Symbol] :=
429 Int[(A_+B_.*Tanh[c_.+d_.*x_])/Sqrt[a_.+b_.*Tanh[c_.+d_.*x_]],x_Symbol] :=
457 …Tanh[c+d x])/Sqrt[a+b Tanh[c+d x]] \[DifferentialD]x \[LongRightArrow] ((A+B)/2)\[Integral](1+Ta…
466 Dist[(A+B)/2,Int[(1+Tanh[c+d*x])/Sqrt[a+b*Tanh[c+d*x]],x]] +
467 Dist[(A-B)/2,Int[(1-Tanh[c+d*x])/Sqrt[a+b*Tanh[c+d*x]],x]] /;
492 (*-((B (a+b Tanh[c+d x])^n)/(d n))+\[Integral](a A+b B+(b A+a B) Tanh[c+d x])(a+b Tanh[c+d x])^(n-1…
502 Int[(a*A+b*B+(b*A+a*B)*Tanh[c+d*x])*(a+b*Tanh[c+d*x])^(n-1),x] /;
[all …]
H A DHyperbolicSubstitution.m128 Int[u_*Tanh[c_.*(a_.+b_.*x_)],x_Symbol] :=
195 Int[u_*Tanh[c_.*(a_.+b_.*x_)]^n_.,x_Symbol] :=
246 (*\[Integral]f[Tanh[u]]\!\( *)
255 (*Basis: f[Tanh[z]] Sech[z]^2=f[Tanh[z]] \!\( *)
273 Dist[1/(b*c),Subst[Int[Regularize[SubstFor[Tanh[c*(a+b*x)],u,x],x],x],x,Tanh[c*(a+b*x)]]] /;
286 …sis: If n\[Element]\[DoubleStruckCapitalZ], then f[Tanh[z]] Coth[z]^n=f[Tanh[z]]/(Tanh[z]^n (1-Ta…
304 …Dist[1/(b*c),Subst[Int[Regularize[SubstFor[Tanh[c*(a+b*x)],u,x]/(x^n*(1-x^2)),x],x],x,Tanh[c*(a+b*…
317 (*Basis: f[Tanh[z]]=f[Tanh[z]]/(1-Tanh[z]^2) \!\( *)
338 ShowStep["","Int[f[Tanh[a+b*x]],x]","Subst[Int[f[x]/(1-x^2),x],x,Tanh[a+b*x]]/b",Hold[
339 …Dist[1/Coefficient[v,x,1],Subst[Int[Regularize[SubstFor[Tanh[v],u,x]/(1-x^2),x],x],x,Tanh[v]]]]] /;
[all …]
H A DTwoHyperbolicFunctions.m54 (*Basis: Sinh[z] Tanh[z]=Cosh[z]-Sech[z]*)
94 (*\[Integral]Sinh[a+b x]^m Tanh[a+b x]^n \[DifferentialD]x \[LongRightArrow] ((Sinh[a+b x]^m Tanh…
103 Sinh[a+b*x]^m*Tanh[a+b*x]^(n-1)/(b*m) /;
181 Sinh[a+b*x]^m*Tanh[a+b*x]^(n+1)/(b*m) -
257 Sinh[a+b*x]^m*Tanh[a+b*x]^(n-1)/(b*m) -
481 …Sinh[v] Tanh[w]^n \[DifferentialD]x \[LongRightArrow] \[Integral]u Cosh[v] Tanh[w]^(n-1) \[Diffe…
489 Int[u_.*Sinh[v_]*Tanh[w_]^n_.,x_Symbol] :=
490 Int[u*Cosh[v]*Tanh[w]^(n-1),x] - Cosh[v-w]*Int[u*Sech[w]*Tanh[w]^(n-1),x] /;
539 Int[u_.*Cosh[v_]*Tanh[w_]^n_.,x_Symbol] :=
540 Int[u*Sinh[v]*Tanh[w]^(n-1),x] - Sinh[v-w]*Int[u*Sech[w]*Tanh[w]^(n-1),x] /;
[all …]
/dports/math/blaze/blaze-3.8/blaze/math/functors/
H A DTanh.h80 struct Tanh struct
140 struct YieldsUniform<Tanh,T> argument
158 struct YieldsSymmetric<Tanh,MT>
176 struct YieldsHermitian<Tanh,MT>
194 struct YieldsLower<Tanh,MT>
212 struct YieldsStrictlyLower<Tanh,MT>
230 struct YieldsUpper<Tanh,MT>
248 struct YieldsStrictlyUpper<Tanh,MT>
266 struct YieldsZero<Tanh,T>
/dports/misc/mnn/MNN-1.2.0/tools/converter/source/caffe/
H A DTanh.cpp11 class Tanh : public OpConverter { class
14 Tanh() { in Tanh() function in Tanh
16 virtual ~Tanh() { in ~Tanh()
26 void Tanh::run(MNN::OpT* dstOp, const caffe::LayerParameter& parameters, const caffe::LayerParamete… in run()
29 static OpConverterRegister<Tanh> a("TanH");
/dports/math/fastops/fastops-1.0.0/fastops/
H A Dfastops.cpp77 void Tanh(const float* from, size_t size, float* to) { in Tanh() function
88 void Tanh(const double* from, size_t size, double* to) { in Tanh() function
128 template void Tanh<false, false>(const float* from, size_t size, float* to);
129 template void Tanh<false, true>(const float* from, size_t size, float* to);
130 template void Tanh<true, false>(const float* from, size_t size, float* to);
131 template void Tanh<true, true>(const float* from, size_t size, float* to);
133 template void Tanh<false, false>(const double* from, size_t size, double* to);
134 template void Tanh<false, true>(const double* from, size_t size, double* to);
135 template void Tanh<true, false>(const double* from, size_t size, double* to);
136 template void Tanh<true, true>(const double* from, size_t size, double* to);
/dports/math/reduce/Reduce-svn5758-src/contrib/rubi-red/rubi4/IntegrationRules/MathematicaNotebookFiles/HyperbolicFunctions/
H A DHyperbolicTangentFunctions.nb27 RowBox[{"Tanh", "[",
92 RowBox[{"Tanh", "[",
131 RowBox[{"Tanh", "[",
231 RowBox[{"Tanh", "[",
237 RowBox[{"Tanh", "[",
277 RowBox[{"Tanh", "[",
284 RowBox[{"Tanh", "[",
4284 RowBox[{"Tanh", "[",
4364 RowBox[{"Tanh", "[",
4832 RowBox[{"Tanh", "[",
[all …]
/dports/math/reduce/Reduce-svn5758-src/packages/rubi_red/tests4/InverseHyperbolicFunctions/
H A DInverseHyperbolicTangentFunctions.m988 …Tanh[a + b*x]]^4/x^1, x, 5, (-b)*x*(b*x - ArcTanh[Tanh[a + b*x]])^3 + (1/2)*(b*x - ArcTanh[Tanh[a …
989 …Tanh[a + b*x]]^4/x^2, x, 5, 4*b^2*x*(b*x - ArcTanh[Tanh[a + b*x]])^2 - 2*b*(b*x - ArcTanh[Tanh[a +…
995 …Tanh[a + b*x]]^4/x^8, x, 3, (b^2*ArcTanh[Tanh[a + b*x]]^5)/(105*x^5*(b*x - ArcTanh[Tanh[a + b*x]])…
1026 …Tanh[a + b*x]]^2/x^1, x, 5, -(1/((b*x - ArcTanh[Tanh[a + b*x]])*ArcTanh[Tanh[a + b*x]])) + Log[x]/…
1027 …Tanh[a + b*x]]^2/x^2, x, 6, -((2*b)/((b*x - ArcTanh[Tanh[a + b*x]])^2*ArcTanh[Tanh[a + b*x]])) + 1…
1028 …Tanh[a + b*x]]^2/x^3, x, 7, -((3*b^2)/((b*x - ArcTanh[Tanh[a + b*x]])^3*ArcTanh[Tanh[a + b*x]])) +…
1038 …Tanh[a + b*x]]^3/x^1, x, 6, -(1/(2*(b*x - ArcTanh[Tanh[a + b*x]])*ArcTanh[Tanh[a + b*x]]^2)) + 1/(…
1039 …Tanh[a + b*x]]^3/x^2, x, 7, -((3*b)/(2*(b*x - ArcTanh[Tanh[a + b*x]])^2*ArcTanh[Tanh[a + b*x]]^2))…
1040 …Tanh[a + b*x]]^3/x^3, x, 8, -((3*b^2)/((b*x - ArcTanh[Tanh[a + b*x]])^3*ArcTanh[Tanh[a + b*x]]^2))…
1078 …Tanh[a + b*x]]^(5/2)/x^1, x, 4, -2*ArcTan[Sqrt[ArcTanh[Tanh[a + b*x]]]/Sqrt[b*x - ArcTanh[Tanh[a +…
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