| /dports/math/reduce/Reduce-svn5758-src/packages/rubi_red/tests4/HyperbolicFunctions/ |
| H A D | HyperbolicCotangentFunctions.m | 20 {Coth[a + b*x]^4, x, 3, x - Coth[a + b*x]/b - Coth[a + b*x]^3/(3*b)}
22 {Coth[a + b*x]^6, x, 4, x - Coth[a + b*x]/b - Coth[a + b*x]^3/(3*b) - Coth[a + b*x]^5/(5*b)}
107 …Coth[c + d*x]^3)^(1/2), x, 6, -((2*Coth[c + d*x])/(d*Sqrt[b*Coth[c + d*x]^3])) - (ArcTan[Sqrt[Coth…
116 …Coth[c + d*x]^3)^(4/3), x, 4, -(Coth[c + d*x]/(3*d*(b*Coth[c + d*x]^3)^(4/3))) - Coth[c + d*x]^3/(…
198 {Csch[x]^4/(1 + Coth[x]), x, 3, Coth[x] - Coth[x]^2/2}
284 {Coth[x]^2/(1 + Coth[x]), x, 3, x/2 - 1/(2*(1 + Coth[x])) - Log[1 + Coth[x]]}
285 {Coth[x]^3/(1 + Coth[x]), x, 4, (3*x)/2 - (3*Coth[x])/2 + Coth[x]^2/(2*(1 + Coth[x])) - Log[Sinh[x]…
286 {Coth[x]^4/(1 + Coth[x]), x, 5, -((3*x)/2) + (3*Coth[x])/2 - Coth[x]^2 + Coth[x]^3/(2*(1 + Coth[x])…
349 {1/Sqrt[1 - Coth[x]^2], x, 2, Coth[x]/Sqrt[-Csch[x]^2], Coth[x]/Sqrt[1 - Coth[x]^2]}
352 {(-1 + Coth[x]^2)^(3/2), x, 4, (1/2)*ArcTanh[Coth[x]/Sqrt[-1 + Coth[x]^2]] - (1/2)*Coth[x]*Sqrt[-1 …
[all …]
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| H A D | HyperbolicCosecantFunctions.m | 20 {Csch[a + b*x]^6, x, 2, -(Coth[a + b*x]/b) + (2*Coth[a + b*x]^3)/(3*b) - Coth[a + b*x]^5/(5*b)}
59 {(-Csch[x]^2)^(5/2), x, 4, (3/8)*ArcSin[Coth[x]] + (3/8)*Coth[x]*Sqrt[1 - Coth[x]^2] + (1/4)*Coth[x…
60 {(-Csch[x]^2)^(3/2), x, 3, (1/2)*ArcSin[Coth[x]] + (1/2)*Coth[x]*Sqrt[1 - Coth[x]^2]}
62 {1/(-Csch[x]^2)^(1/2), x, 2, Coth[x]/Sqrt[-Csch[x]^2], Coth[x]/Sqrt[1 - Coth[x]^2]}
63 {1/(-Csch[x]^2)^(3/2), x, 3, Coth[x]/(3*(1 - Coth[x]^2)^(3/2)) + (2*Coth[x])/(3*Sqrt[1 - Coth[x]^2]…
64 …sch[x]^2)^(5/2), x, 4, Coth[x]/(5*(1 - Coth[x]^2)^(5/2)) + (4*Coth[x])/(15*(1 - Coth[x]^2)^(3/2)) …
65 …, Coth[x]/(7*(1 - Coth[x]^2)^(7/2)) + (6*Coth[x])/(35*(1 - Coth[x]^2)^(5/2)) + (8*Coth[x])/(35*(1 …
237 … Csch[x]^2)^(3/2), x, 5, 2*ArcSin[Coth[x]/Sqrt[2]] + ArcTanh[Coth[x]/Sqrt[2 - Coth[x]^2]] + (1/2)*…
242 …]^2)^(3/2), x, 5, ArcTan[Coth[x]/Sqrt[-2 + Coth[x]^2]] + 2*ArcTanh[Coth[x]/Sqrt[-2 + Coth[x]^2]] -…
243 {Sqrt[-1 + Csch[x]^2], x, 4, -ArcTan[Coth[x]/Sqrt[-2 + Coth[x]^2]] - ArcTanh[Coth[x]/Sqrt[-2 + Coth…
[all …]
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| H A D | HyperbolicFunctions.m | 159 …Coth[x]^5/Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4], x, 9, (b*ArcTanh[(b + 2*c*Coth[x]^2)/(2*Sqrt[c]*Sqr…
160 …Coth[x]^3/Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4], x, 6, -(ArcTanh[(b + 2*c*Coth[x]^2)/(2*Sqrt[c]*Sqrt…
161 {Coth[x]/Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4], x, 4, ArcTanh[(2*a + b + (b + 2*c)*Coth[x]^2)/(2*Sqrt…
162 …Coth[x]^2 + c*Coth[x]^4], x, 7, -(ArcTanh[(2*a + b*Coth[x]^2)/(2*Sqrt[a]*Sqrt[a + b*Coth[x]^2 + c*…
163 …Coth[x]^2 + c*Coth[x]^4], x, 12, -(ArcTanh[(2*a + b*Coth[x]^2)/(2*Sqrt[a]*Sqrt[a + b*Coth[x]^2 + c…
173 (* {Coth[x]^5*Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4], x, 0, 0} *)
174 (* {Coth[x]^3*Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4], x, 0, 0} *)
175 …Coth[x]*Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4], x, 7, -(((b + 2*c)*ArcTanh[(b + 2*c*Coth[x]^2)/(2*Sqr…
453 {Csch[x]^2*(a + b*Coth[x])/(c + d*Coth[x]), x, 4, -((b*Coth[x])/d) + ((b*c - a*d)*Log[c + d*Coth[x]…
454 …Csch[x]^2*(a + b*Coth[x])^2/(c + d*Coth[x]), x, 5, (b*(b*c - a*d)*Coth[x])/d^2 - (a + b*Coth[x])^2…
[all …]
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| H A D | tanh^3.m | 22 {Csch[c + d*x]^4*(a + b*Tanh[c + d*x]^3), x, 7, (a*Coth[c + d*x])/d - (b*Coth[c + d*x])/d - (a*Coth…
170 {Coth[c + d*x]^2*(a + b*Tanh[c + d*x]^3), x, 2, (a + b)*x - (a*Coth[c + d*x])/d}
171 {Coth[c + d*x]^3*(a + b*Tanh[c + d*x]^3), x, 2, -(a*Coth[c + d*x]^2)/(2*d) + ((a + b)*Log[Sinh[c + …
172 {Coth[c + d*x]^4*(a + b*Tanh[c + d*x]^3), x, 3, (a + b)*x - ((a + b)*Coth[c + d*x])/d - (a*Coth[c +…
173 {Coth[c + d*x]^5*(a + b*Tanh[c + d*x]^3), x, 3, -(((a + b)*Coth[c + d*x]^2)/(2*d)) - (a*Coth[c + d*…
182 {Coth[c + d*x]^2*(a + b*Tanh[c + d*x]^3)^2, x, 4, (a + b)^2*x - (a^2*Coth[c + d*x])/d - (b^2*Tanh[c…
184 {Coth[c + d*x]^4*(a + b*Tanh[c + d*x]^3)^2, x, 4, (a + b)^2*x - (a*(a + 2*b)*Coth[c + d*x])/d - (a^…
186 {Coth[c + d*x]^6*(a + b*Tanh[c + d*x]^3)^2, x, 4, (a + b)^2*x - ((a + b)^2*Coth[c + d*x])/d - (a*(a…
187 {Coth[c + d*x]^7*(a + b*Tanh[c + d*x]^3)^2, x, 4, -(((a + b)^2*Coth[c + d*x]^2)/(2*d)) - (a*(a + 2*…
198 {Coth[c + d*x]^4*(a + b*Tanh[c + d*x]^3)^3, x, 4, (a + b)^3*x - (a^2*(a + 3*b)*Coth[c + d*x])/d - (…
[all …]
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| H A D | HyperbolicSineFunctions.m | 153 …+ Sinh[x]), x, 5, (3/2)*ArcTanh[Cosh[x]] - 4*I*Coth[x] + (4/3)*I*Coth[x]^3 - (3/2)*Coth[x]*Csch[x]…
163 …-5*I*ArcTanh[Cosh[x]] - 12*Coth[x] + 4*Coth[x]^3 + 5*I*Coth[x]*Csch[x] + (Coth[x]*Csch[x]^2)/(3*(I…
333 {Coth[x]^2/(I + Sinh[x]), x, 2, -ArcTanh[Cosh[x]] + I*Coth[x]}
335 {Coth[x]^4/(I + Sinh[x]), x, 3, (-(1/2))*ArcTanh[Cosh[x]] + (1/3)*I*Coth[x]^3 - (1/2)*Coth[x]*Csch[…
337 {Coth[x]^6/(I + Sinh[x]), x, 4, (-(3/8))*ArcTanh[Cosh[x]] + (1/5)*I*Coth[x]^5 - (3/8)*Coth[x]*Csch[…
347 {Coth[x]^4/(I + Sinh[x])^2, x, 5, (-I)*ArcTanh[Cosh[x]] - 2*Coth[x] + Coth[x]^3/3 + I*Coth[x]*Csch[…
349 {Coth[x]^6/(I + Sinh[x])^2, x, 7, (-(1/4))*I*ArcTanh[Cosh[x]] - (2*Coth[x]^3)/3 + Coth[x]^5/5 - (1/…
403 …Coth[c + d*x])/(48*d*(1 - Coth[c + d*x]^2)^3) + ((48*a^2 - 80*a*b + 35*b^2)*Coth[c + d*x])/(192*d*…
405 …Coth[c + d*x])/(24*d*(1 - Coth[c + d*x]^2)^2) - ((8*a^2 - 12*a*b + 5*b^2)*Coth[c + d*x])/(16*d*(1 …
737 …*(a + b*Sinh[c + d*x]^4), x, 5, -((a*Coth[c + d*x])/d) - (b*Coth[c + d*x])/d + (2*a*Coth[c + d*x]^…
[all …]
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| H A D | HyperbolicTangentFunctions.m | 100 {Sqrt[a*Tanh[x]^4], x, 3, (-Coth[x])*Sqrt[a*Tanh[x]^4] + x*Coth[x]^2*Sqrt[a*Tanh[x]^4]}
127 {Csch[x]^4/(1 + Tanh[x]), x, 4, Coth[x]^2/2 - Coth[x]^3/3}
129 {Csch[x]^6/(1 + Tanh[x]), x, 4, (-(1/2))*Coth[x]^2 + Coth[x]^3/3 + Coth[x]^4/4 - Coth[x]^5/5}
206 {Coth[x]^2/(1 + Tanh[x]), x, 4, (3*x)/2 - (3*Coth[x])/2 - Log[Sinh[x]] + Coth[x]/(2*(1 + Tanh[x]))}
207 {Coth[x]^3/(1 + Tanh[x]), x, 5, -((3*x)/2) + (3*Coth[x])/2 - Coth[x]^2 + 2*Log[Sinh[x]] + Coth[x]^2…
208 {Coth[x]^4/(1 + Tanh[x]), x, 6, (5*x)/2 - (5*Coth[x])/2 + Coth[x]^2 - (5*Coth[x]^3)/6 - 2*Log[Sinh[…
442 {Coth[c + d*x]^2*(a + b*Tanh[c + d*x]^2), x, 2, (a + b)*x - (a*Coth[c + d*x])/d}
444 {Coth[c + d*x]^4*(a + b*Tanh[c + d*x]^2), x, 3, (a + b)*x - ((a + b)*Coth[c + d*x])/d - (a*Coth[c +…
456 {Coth[c + d*x]^4*(a + b*Tanh[c + d*x]^2)^2, x, 4, (a + b)^2*x - (a*(a + 2*b)*Coth[c + d*x])/d - (a^…
458 {Coth[c + d*x]^6*(a + b*Tanh[c + d*x]^2)^2, x, 4, (a + b)^2*x - ((a + b)^2*Coth[c + d*x])/d - (a*(a…
[all …]
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| H A D | TwoHyperbolicFunctions.m | 181 {Coth[x]^2*Csch[x]^4, x, 3, Coth[x]^3/3 - Coth[x]^5/5}
182 {Coth[x]^3*Csch[x]^4, x, 3, Coth[x]^4/4 - Coth[x]^6/6}
183 {Coth[x]^n*Csch[x]^4, x, 4, Coth[x]^(1 + n)/(1 + n) - Coth[x]^(3 + n)/(3 + n)}
185 {Coth[x]^4*Csch[x]^3, x, 4, (1/16)*ArcTanh[Cosh[x]] + (1/16)*Coth[x]*Csch[x] + (1/24)*Coth[x]^3*Csc…
186 {Coth[x]^4*Csch[x]^6, x, 3, (-(1/5))*Coth[x]^5 + (2*Coth[x]^7)/7 - Coth[x]^9/9}
879 …osh[x]*Coth[x])^(5/2), x, 6, (-(16/15))*Coth[x]*Sqrt[Cosh[x]*Coth[x]] + (2/5)*Cosh[x]^2*Coth[x]*Sq…
1014 {(a*Coth[x] + b*Csch[x])^2, x, 7, a^2*x - a^2*Coth[x] - b^2*Coth[x] - 2*a*b*Csch[x]}
1027 {(Coth[x] + Csch[x])^2, x, 3, x - 2*Coth[x/2]}
1029 {(Coth[x] + Csch[x])^4, x, 4, x - 2*Coth[x/2] - (2/3)*Coth[x/2]^3}
1048 {1/(-Coth[x] + Csch[x])^4, x, 4, x - 2*Coth[x/2] - (2/3)*Coth[x/2]^3}
[all …]
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| H A D | HyperbolicSecantFunctions.m | 131 {Csch[x]^4/(a + a*Sech[x]), x, 4, Coth[x]^3/(3*a) - Coth[x]^5/(5*a) + Csch[x]^5/(5*a)}
226 {Coth[x]^1/(a + a*Sech[x]), x, 5, ArcTanh[Cosh[x]]/(2*a) - Coth[x]^2/(2*a) + (Coth[x]*Csch[x])/(2*a…
227 {Coth[x]^2/(a + a*Sech[x]), x, 6, x/a - Coth[x]/a - Coth[x]^3/(3*a) + Csch[x]/a + Csch[x]^3/(3*a)}
228 {Coth[x]^3/(a + a*Sech[x]), x, 7, (3*ArcTanh[Cosh[x]])/(8*a) - Coth[x]^2/(2*a) - Coth[x]^4/(4*a) + …
229 {Coth[x]^4/(a + a*Sech[x]), x, 8, x/a - Coth[x]/a - Coth[x]^3/(3*a) - Coth[x]^5/(5*a) + Csch[x]/a +…
269 …^4*(a + b*Sech[c + d*x]^2), x, 7, (a*Coth[c + d*x])/d + (2*b*Coth[c + d*x])/d - (a*Coth[c + d*x]^3…
417 {Coth[c + d*x]^2*(a + b*Sech[c + d*x]^2), x, 3, a*x - ((a + b)*Coth[c + d*x])/d}
419 {Coth[c + d*x]^4*(a + b*Sech[c + d*x]^2), x, 4, a*x - (a*Coth[c + d*x])/d - ((a + b)*Coth[c + d*x]^…
431 {Coth[c + d*x]^4*(a + b*Sech[c + d*x]^2)^2, x, 4, a^2*x - ((a^2 - b^2)*Coth[c + d*x])/d - ((a + b)^…
433 {Coth[c + d*x]^6*(a + b*Sech[c + d*x]^2)^2, x, 4, a^2*x - (a^2*Coth[c + d*x])/d - ((a^2 - b^2)*Coth…
[all …]
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| /dports/math/reduce/Reduce-svn5758-src/packages/rubi_red/tests/HyperbolicFunctions/ |
| H A D | HyperbolicCotangentFunctions.m | 13 {Coth[a+b*x]^2, x, 1, x - Coth[a+b*x]/b}
15 {Coth[a+b*x]^4, x, 2, x - Coth[a + b*x]/b - Coth[a + b*x]^3/(3*b)}
21 {Coth[a+b*x]^(3/2), x, 6, ArcTan[Sqrt[Coth[a + b*x]]]/b + ArcTanh[Sqrt[Coth[a + b*x]]]/b - (2*Sqrt[…
68 {Sqrt[a*Coth[x]^3], x, 8, ((ArcTan[Sqrt[Coth[x]]] + ArcTanh[Sqrt[Coth[x]]] - 2*Sqrt[Coth[x]])*Sqrt[…
73 …(a*Coth[x]^3)^(3/2),x, 9, -((a*Sqrt[a*Coth[x]^3]*(21*ArcTan[Sqrt[Coth[x]]] - 21*ArcTanh[Sqrt[Coth[…
74 {(a*Coth[x]^4)^(3/2),x, 4, (-(1/3))*a*Coth[x]*Sqrt[a*Coth[x]^4] - (1/5)*a*Coth[x]^3*Sqrt[a*Coth[x]^…
78 {1/Sqrt[a*Coth[x]^3], x, 10, -(((2 + (ArcTan[Sqrt[Coth[x]]] - ArcTanh[Sqrt[Coth[x]]])*Sqrt[Coth[x]]…
79 {1/Sqrt[a*Coth[x]^4], x, 2, -(Coth[x]/Sqrt[a*Coth[x]^4]) + (x*Coth[x]^2)/Sqrt[a*Coth[x]^4]}
91 {1/(1 + Coth[x])^3, x, 3, x/8 - 1/(6*(1 + Coth[x])^3) - 1/(8*(1 + Coth[x])^2) - 1/(8*(1 + Coth[x]))}
130 {Sqrt[-1 - Coth[x]^2], x, 4, ArcTan[Coth[x]/Sqrt[-1 - Coth[x]^2]] - Sqrt[2]*ArcTan[(Sqrt[2]*Coth[x]…
[all …]
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| H A D | HyperbolicCosecantFunctions.m | 15 {Csch[a+b*x]^4, x, 2, Coth[a + b*x]/b - Coth[a + b*x]^3/(3*b)}
97 … 4, -((a^3*Cosh[x]*(3003 - 6006*Coth[x]^2 + 9009*Coth[x]^4 - 8580*Coth[x]^6 + 5005*Coth[x]^8 - 163…
98 …^4)^(5/2), x, 4, (-(1/315))*a^2*Cosh[x]*(315 - 420*Coth[x]^2 + 378*Coth[x]^4 - 180*Coth[x]^6 + 35*…
146 {(a + b*Csch[x]^2)^2, x, 5, a^2*x - 2*a*b*Coth[x] + b^2*Coth[x] - (1/3)*b^2*Coth[x]^3}
147 …2)^3, x, 8, a^3*x - 3*a^2*b*Coth[x] + 3*a*b^2*Coth[x] - b^3*Coth[x] - a*b^2*Coth[x]^3 + (2/3)*b^3*…
156 {Sqrt[1 - Csch[x]^2], x, 4, ArcSin[Coth[x]/Sqrt[2]] + ArcTanh[Coth[x]/Sqrt[2 - Coth[x]^2]]}
157 {Sqrt[-1 + Csch[x]^2], x, 4, -ArcTan[Coth[x]/Sqrt[-2 + Coth[x]^2]] - ArcTanh[Coth[x]/Sqrt[-2 + Coth…
162 {1/Sqrt[1 - Csch[x]^2], x, 2, ArcTanh[Coth[x]/Sqrt[2 - Coth[x]^2]]}
168 … Csch[x]^2)^(3/2), x, 7, 2*ArcSin[Coth[x]/Sqrt[2]] + ArcTanh[Coth[x]/Sqrt[2 - Coth[x]^2]] + (1/2)*…
169 …]^2)^(3/2), x, 8, ArcTan[Coth[x]/Sqrt[-2 + Coth[x]^2]] + 2*ArcTanh[Coth[x]/Sqrt[-2 + Coth[x]^2]] -…
[all …]
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| H A D | TwoHyperbolicFunctions.m | 171 {Coth[x]^2*Csch[x]^4, x, 3, Coth[x]^3/3 - Coth[x]^5/5}
172 {Coth[x]^3*Csch[x]^4, x, 3, Coth[x]^4/4 - Coth[x]^6/6}
176 {Coth[x]^4*Csch[x]^6, x, 3, (-(1/5))*Coth[x]^5 + (2*Coth[x]^7)/7 - Coth[x]^9/9}
862 {Coth[x]/(1 + Coth[x]), x, 2, x/2 + 1/(2*(1 + Coth[x]))}
892 {Csch[x]^4/(1 + Coth[x]), x, 2, Coth[x] - Coth[x]^2/2}
1322 {Coth[x]*(1 + Coth[x])^(3/2), x, 3, 2*Sqrt[2]*ArcCoth[Sqrt[1 + Coth[x]]/Sqrt[2]] - 2*Sqrt[1 + Coth[…
1323 {Coth[x]*Sqrt[1 + Coth[x]], x, 2, Sqrt[2]*ArcCoth[Sqrt[1 + Coth[x]]/Sqrt[2]] - 2*Sqrt[1 + Coth[x]]}
1329 {Coth[x]^2/Sqrt[1 + Coth[x]], x, 6, ArcTanh[Sqrt[1 + Coth[x]]/Sqrt[2]]/Sqrt[2] - 1/Sqrt[1 + Coth[x]…
1430 …Coth[x]^2*(a + b*Coth[x]^2)^(3/2), x, 13, -((3*a^2*ArcTanh[(Sqrt[b]*Coth[x])/Sqrt[a + b*Coth[x]^2]…
1438 {Coth[x]^2/(a + b*Coth[x]^2)^(3/2), x, 7, ArcTanh[(Sqrt[a + b]*Coth[x])/Sqrt[a + b*Coth[x]^2]]/(a +…
[all …]
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| H A D | HyperbolicFunctions.m | 174 …Coth[x]^5/Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4], x, 9, (b*ArcTanh[(b + 2*c*Coth[x]^2)/(2*Sqrt[c]*Sqr…
175 …Coth[x]^3/Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4], x, 7, -(ArcTanh[(b + 2*c*Coth[x]^2)/(2*Sqrt[c]*Sqrt…
176 {Coth[x]/Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4], x, 4, ArcTanh[(2*a + b + (b + 2*c)*Coth[x]^2)/(2*Sqrt…
177 …Coth[x]^2 + c*Coth[x]^4], x, 6, -(ArcTanh[(2*a + b*Coth[x]^2)/(2*Sqrt[a]*Sqrt[a + b*Coth[x]^2 + c*…
178 …Coth[x]^2 + c*Coth[x]^4], x, 9, -(ArcTanh[(2*a + b*Coth[x]^2)/(2*Sqrt[a]*Sqrt[a + b*Coth[x]^2 + c*…
188 (* {Coth[x]^5*Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4], x, 0, 0} *)
189 (* {Coth[x]^3*Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4], x, 0, 0} *)
190 …Coth[x]*Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4], x, 6, -(((b + 2*c)*ArcTanh[(b + 2*c*Coth[x]^2)/(2*Sqr…
471 {Csch[x]^2*(a + b*Coth[x])/(c + d*Coth[x]), x, 4, -((b*Coth[x])/d) + ((b*c - a*d)*Log[c + d*Coth[x]…
472 …Csch[x]^2*(a + b*Coth[x])^2/(c + d*Coth[x]), x, 5, (b*(b*c - a*d)*Coth[x])/d^2 - (a + b*Coth[x])^2…
[all …]
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| /dports/math/reduce/Reduce-svn5758-src/contrib/rubi-red/rubi4/IntegrationProblems/MathematicaSyntaxFiles/HyperbolicFunctions/ |
| H A D | HyperbolicCotangentFunctions.m | 13 {Coth[a+b*x]^2, x, 1, x - Coth[a+b*x]/b}
15 {Coth[a+b*x]^4, x, 2, x - Coth[a + b*x]/b - Coth[a + b*x]^3/(3*b)}
21 {Coth[a+b*x]^(3/2), x, 6, ArcTan[Sqrt[Coth[a + b*x]]]/b + ArcTanh[Sqrt[Coth[a + b*x]]]/b - (2*Sqrt[…
68 {Sqrt[a*Coth[x]^3], x, 8, ((ArcTan[Sqrt[Coth[x]]] + ArcTanh[Sqrt[Coth[x]]] - 2*Sqrt[Coth[x]])*Sqrt[…
73 …(a*Coth[x]^3)^(3/2),x, 9, -((a*Sqrt[a*Coth[x]^3]*(21*ArcTan[Sqrt[Coth[x]]] - 21*ArcTanh[Sqrt[Coth[…
74 {(a*Coth[x]^4)^(3/2),x, 4, (-(1/3))*a*Coth[x]*Sqrt[a*Coth[x]^4] - (1/5)*a*Coth[x]^3*Sqrt[a*Coth[x]^…
78 {1/Sqrt[a*Coth[x]^3], x, 10, -(((2 + (ArcTan[Sqrt[Coth[x]]] - ArcTanh[Sqrt[Coth[x]]])*Sqrt[Coth[x]]…
79 {1/Sqrt[a*Coth[x]^4], x, 2, -(Coth[x]/Sqrt[a*Coth[x]^4]) + (x*Coth[x]^2)/Sqrt[a*Coth[x]^4]}
91 {1/(1 + Coth[x])^3, x, 3, x/8 - 1/(6*(1 + Coth[x])^3) - 1/(8*(1 + Coth[x])^2) - 1/(8*(1 + Coth[x]))}
130 {Sqrt[-1 - Coth[x]^2], x, 4, ArcTan[Coth[x]/Sqrt[-1 - Coth[x]^2]] - Sqrt[2]*ArcTan[(Sqrt[2]*Coth[x]…
[all …]
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| H A D | HyperbolicCosecantFunctions.m | 15 {Csch[a+b*x]^4, x, 2, Coth[a + b*x]/b - Coth[a + b*x]^3/(3*b)}
97 … 4, -((a^3*Cosh[x]*(3003 - 6006*Coth[x]^2 + 9009*Coth[x]^4 - 8580*Coth[x]^6 + 5005*Coth[x]^8 - 163…
98 …^4)^(5/2), x, 4, (-(1/315))*a^2*Cosh[x]*(315 - 420*Coth[x]^2 + 378*Coth[x]^4 - 180*Coth[x]^6 + 35*…
146 {(a + b*Csch[x]^2)^2, x, 5, a^2*x - 2*a*b*Coth[x] + b^2*Coth[x] - (1/3)*b^2*Coth[x]^3}
147 …2)^3, x, 8, a^3*x - 3*a^2*b*Coth[x] + 3*a*b^2*Coth[x] - b^3*Coth[x] - a*b^2*Coth[x]^3 + (2/3)*b^3*…
156 {Sqrt[1 - Csch[x]^2], x, 4, ArcSin[Coth[x]/Sqrt[2]] + ArcTanh[Coth[x]/Sqrt[2 - Coth[x]^2]]}
157 {Sqrt[-1 + Csch[x]^2], x, 4, -ArcTan[Coth[x]/Sqrt[-2 + Coth[x]^2]] - ArcTanh[Coth[x]/Sqrt[-2 + Coth…
162 {1/Sqrt[1 - Csch[x]^2], x, 2, ArcTanh[Coth[x]/Sqrt[2 - Coth[x]^2]]}
168 … Csch[x]^2)^(3/2), x, 7, 2*ArcSin[Coth[x]/Sqrt[2]] + ArcTanh[Coth[x]/Sqrt[2 - Coth[x]^2]] + (1/2)*…
169 …]^2)^(3/2), x, 8, ArcTan[Coth[x]/Sqrt[-2 + Coth[x]^2]] + 2*ArcTanh[Coth[x]/Sqrt[-2 + Coth[x]^2]] -…
[all …]
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| H A D | TwoHyperbolicFunctions.m | 171 {Coth[x]^2*Csch[x]^4, x, 3, Coth[x]^3/3 - Coth[x]^5/5}
172 {Coth[x]^3*Csch[x]^4, x, 3, Coth[x]^4/4 - Coth[x]^6/6}
176 {Coth[x]^4*Csch[x]^6, x, 3, (-(1/5))*Coth[x]^5 + (2*Coth[x]^7)/7 - Coth[x]^9/9}
862 {Coth[x]/(1 + Coth[x]), x, 2, x/2 + 1/(2*(1 + Coth[x]))}
892 {Csch[x]^4/(1 + Coth[x]), x, 2, Coth[x] - Coth[x]^2/2}
1322 {Coth[x]*(1 + Coth[x])^(3/2), x, 3, 2*Sqrt[2]*ArcCoth[Sqrt[1 + Coth[x]]/Sqrt[2]] - 2*Sqrt[1 + Coth[…
1323 {Coth[x]*Sqrt[1 + Coth[x]], x, 2, Sqrt[2]*ArcCoth[Sqrt[1 + Coth[x]]/Sqrt[2]] - 2*Sqrt[1 + Coth[x]]}
1329 {Coth[x]^2/Sqrt[1 + Coth[x]], x, 6, ArcTanh[Sqrt[1 + Coth[x]]/Sqrt[2]]/Sqrt[2] - 1/Sqrt[1 + Coth[x]…
1430 …Coth[x]^2*(a + b*Coth[x]^2)^(3/2), x, 13, -((3*a^2*ArcTanh[(Sqrt[b]*Coth[x])/Sqrt[a + b*Coth[x]^2]…
1438 {Coth[x]^2/(a + b*Coth[x]^2)^(3/2), x, 7, ArcTanh[(Sqrt[a + b]*Coth[x])/Sqrt[a + b*Coth[x]^2]]/(a +…
[all …]
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| H A D | HyperbolicFunctions.m | 174 …Coth[x]^5/Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4], x, 9, (b*ArcTanh[(b + 2*c*Coth[x]^2)/(2*Sqrt[c]*Sqr…
175 …Coth[x]^3/Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4], x, 7, -(ArcTanh[(b + 2*c*Coth[x]^2)/(2*Sqrt[c]*Sqrt…
176 {Coth[x]/Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4], x, 4, ArcTanh[(2*a + b + (b + 2*c)*Coth[x]^2)/(2*Sqrt…
177 …Coth[x]^2 + c*Coth[x]^4], x, 6, -(ArcTanh[(2*a + b*Coth[x]^2)/(2*Sqrt[a]*Sqrt[a + b*Coth[x]^2 + c*…
178 …Coth[x]^2 + c*Coth[x]^4], x, 9, -(ArcTanh[(2*a + b*Coth[x]^2)/(2*Sqrt[a]*Sqrt[a + b*Coth[x]^2 + c*…
188 (* {Coth[x]^5*Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4], x, 0, 0} *)
189 (* {Coth[x]^3*Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4], x, 0, 0} *)
190 …Coth[x]*Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4], x, 6, -(((b + 2*c)*ArcTanh[(b + 2*c*Coth[x]^2)/(2*Sqr…
471 {Csch[x]^2*(a + b*Coth[x])/(c + d*Coth[x]), x, 4, -((b*Coth[x])/d) + ((b*c - a*d)*Log[c + d*Coth[x]…
472 …Csch[x]^2*(a + b*Coth[x])^2/(c + d*Coth[x]), x, 5, (b*(b*c - a*d)*Coth[x])/d^2 - (a + b*Coth[x])^2…
[all …]
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| /dports/math/reduce/Reduce-svn5758-src/contrib/rubi-red/mathematicatests/ |
| H A D | HyperbolicCotangentFunctions.m | 13 {Coth[a+b*x]^2, x, 1, x - Coth[a+b*x]/b}
15 {Coth[a+b*x]^4, x, 2, x - Coth[a + b*x]/b - Coth[a + b*x]^3/(3*b)}
21 {Coth[a+b*x]^(3/2), x, 6, ArcTan[Sqrt[Coth[a + b*x]]]/b + ArcTanh[Sqrt[Coth[a + b*x]]]/b - (2*Sqrt[…
68 {Sqrt[a*Coth[x]^3], x, 8, ((ArcTan[Sqrt[Coth[x]]] + ArcTanh[Sqrt[Coth[x]]] - 2*Sqrt[Coth[x]])*Sqrt[…
73 …(a*Coth[x]^3)^(3/2),x, 9, -((a*Sqrt[a*Coth[x]^3]*(21*ArcTan[Sqrt[Coth[x]]] - 21*ArcTanh[Sqrt[Coth[…
74 {(a*Coth[x]^4)^(3/2),x, 4, (-(1/3))*a*Coth[x]*Sqrt[a*Coth[x]^4] - (1/5)*a*Coth[x]^3*Sqrt[a*Coth[x]^…
78 {1/Sqrt[a*Coth[x]^3], x, 10, -(((2 + (ArcTan[Sqrt[Coth[x]]] - ArcTanh[Sqrt[Coth[x]]])*Sqrt[Coth[x]]…
79 {1/Sqrt[a*Coth[x]^4], x, 2, -(Coth[x]/Sqrt[a*Coth[x]^4]) + (x*Coth[x]^2)/Sqrt[a*Coth[x]^4]}
91 {1/(1 + Coth[x])^3, x, 3, x/8 - 1/(6*(1 + Coth[x])^3) - 1/(8*(1 + Coth[x])^2) - 1/(8*(1 + Coth[x]))}
130 {Sqrt[-1 - Coth[x]^2], x, 4, ArcTan[Coth[x]/Sqrt[-1 - Coth[x]^2]] - Sqrt[2]*ArcTan[(Sqrt[2]*Coth[x]…
[all …]
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| H A D | HyperbolicCosecantFunctions.m | 15 {Csch[a+b*x]^4, x, 2, Coth[a + b*x]/b - Coth[a + b*x]^3/(3*b)}
97 … 4, -((a^3*Cosh[x]*(3003 - 6006*Coth[x]^2 + 9009*Coth[x]^4 - 8580*Coth[x]^6 + 5005*Coth[x]^8 - 163…
98 …^4)^(5/2), x, 4, (-(1/315))*a^2*Cosh[x]*(315 - 420*Coth[x]^2 + 378*Coth[x]^4 - 180*Coth[x]^6 + 35*…
146 {(a + b*Csch[x]^2)^2, x, 5, a^2*x - 2*a*b*Coth[x] + b^2*Coth[x] - (1/3)*b^2*Coth[x]^3}
147 …2)^3, x, 8, a^3*x - 3*a^2*b*Coth[x] + 3*a*b^2*Coth[x] - b^3*Coth[x] - a*b^2*Coth[x]^3 + (2/3)*b^3*…
156 {Sqrt[1 - Csch[x]^2], x, 4, ArcSin[Coth[x]/Sqrt[2]] + ArcTanh[Coth[x]/Sqrt[2 - Coth[x]^2]]}
157 {Sqrt[-1 + Csch[x]^2], x, 4, -ArcTan[Coth[x]/Sqrt[-2 + Coth[x]^2]] - ArcTanh[Coth[x]/Sqrt[-2 + Coth…
162 {1/Sqrt[1 - Csch[x]^2], x, 2, ArcTanh[Coth[x]/Sqrt[2 - Coth[x]^2]]}
168 … Csch[x]^2)^(3/2), x, 7, 2*ArcSin[Coth[x]/Sqrt[2]] + ArcTanh[Coth[x]/Sqrt[2 - Coth[x]^2]] + (1/2)*…
169 …]^2)^(3/2), x, 8, ArcTan[Coth[x]/Sqrt[-2 + Coth[x]^2]] + 2*ArcTanh[Coth[x]/Sqrt[-2 + Coth[x]^2]] -…
[all …]
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| H A D | TwoHyperbolicFunctions.m | 171 {Coth[x]^2*Csch[x]^4, x, 3, Coth[x]^3/3 - Coth[x]^5/5}
172 {Coth[x]^3*Csch[x]^4, x, 3, Coth[x]^4/4 - Coth[x]^6/6}
176 {Coth[x]^4*Csch[x]^6, x, 3, (-(1/5))*Coth[x]^5 + (2*Coth[x]^7)/7 - Coth[x]^9/9}
862 {Coth[x]/(1 + Coth[x]), x, 2, x/2 + 1/(2*(1 + Coth[x]))}
892 {Csch[x]^4/(1 + Coth[x]), x, 2, Coth[x] - Coth[x]^2/2}
1322 {Coth[x]*(1 + Coth[x])^(3/2), x, 3, 2*Sqrt[2]*ArcCoth[Sqrt[1 + Coth[x]]/Sqrt[2]] - 2*Sqrt[1 + Coth[…
1323 {Coth[x]*Sqrt[1 + Coth[x]], x, 2, Sqrt[2]*ArcCoth[Sqrt[1 + Coth[x]]/Sqrt[2]] - 2*Sqrt[1 + Coth[x]]}
1329 {Coth[x]^2/Sqrt[1 + Coth[x]], x, 6, ArcTanh[Sqrt[1 + Coth[x]]/Sqrt[2]]/Sqrt[2] - 1/Sqrt[1 + Coth[x]…
1430 …Coth[x]^2*(a + b*Coth[x]^2)^(3/2), x, 13, -((3*a^2*ArcTanh[(Sqrt[b]*Coth[x])/Sqrt[a + b*Coth[x]^2]…
1438 {Coth[x]^2/(a + b*Coth[x]^2)^(3/2), x, 7, ArcTanh[(Sqrt[a + b]*Coth[x])/Sqrt[a + b*Coth[x]^2]]/(a +…
[all …]
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| H A D | HyperbolicFunctions.m | 174 …Coth[x]^5/Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4], x, 9, (b*ArcTanh[(b + 2*c*Coth[x]^2)/(2*Sqrt[c]*Sqr…
175 …Coth[x]^3/Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4], x, 7, -(ArcTanh[(b + 2*c*Coth[x]^2)/(2*Sqrt[c]*Sqrt…
176 {Coth[x]/Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4], x, 4, ArcTanh[(2*a + b + (b + 2*c)*Coth[x]^2)/(2*Sqrt…
177 …Coth[x]^2 + c*Coth[x]^4], x, 6, -(ArcTanh[(2*a + b*Coth[x]^2)/(2*Sqrt[a]*Sqrt[a + b*Coth[x]^2 + c*…
178 …Coth[x]^2 + c*Coth[x]^4], x, 9, -(ArcTanh[(2*a + b*Coth[x]^2)/(2*Sqrt[a]*Sqrt[a + b*Coth[x]^2 + c*…
188 (* {Coth[x]^5*Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4], x, 0, 0} *)
189 (* {Coth[x]^3*Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4], x, 0, 0} *)
190 …Coth[x]*Sqrt[a + b*Coth[x]^2 + c*Coth[x]^4], x, 6, -(((b + 2*c)*ArcTanh[(b + 2*c*Coth[x]^2)/(2*Sqr…
471 {Csch[x]^2*(a + b*Coth[x])/(c + d*Coth[x]), x, 4, -((b*Coth[x])/d) + ((b*c - a*d)*Log[c + d*Coth[x]…
472 …Csch[x]^2*(a + b*Coth[x])^2/(c + d*Coth[x]), x, 5, (b*(b*c - a*d)*Coth[x])/d^2 - (a + b*Coth[x])^2…
[all …]
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| /dports/math/reduce/Reduce-svn5758-src/packages/rubi_red/rubi-rules/HyperbolicFunctions/ |
| H A D | HyperbolicSubstitution.m | 61 Int[u_*Coth[c_.*(a_.+b_.*x_)],x_Symbol] :=
138 (*\[Integral]f[Coth[u]]\!\( *)
147 (*Basis: f[Coth[z]] Csch[z]^2=-f[Coth[z]] \!\( *)
165 -Dist[1/(b*c),Subst[Int[Regularize[SubstFor[Coth[c*(a+b*x)],u,x],x],x],x,Coth[c*(a+b*x)]]] /;
178 …sis: If n\[Element]\[DoubleStruckCapitalZ], then f[Coth[z]] Tanh[z]^n=f[Coth[z]]/(Coth[z]^n (1-Co…
196 …Dist[1/(b*c),Subst[Int[Regularize[SubstFor[Coth[c*(a+b*x)],u,x]/(x^n*(1-x^2)),x],x],x,Coth[c*(a+b*…
209 (*Basis: f[Coth[z]]=f[Coth[z]]/(1-Coth[z]^2) \!\( *)
230 ShowStep["","Int[f[Coth[a+b*x]],x]","Subst[Int[f[x]/(1-x^2),x],x,Coth[a+b*x]]/b",Hold[
231 …Dist[1/Coefficient[v,x,1],Subst[Int[Regularize[SubstFor[Coth[v],u,x]/(1-x^2),x],x],x,Coth[v]]]]] /;
237 Dist[1/Coefficient[v,x,1],Subst[Int[Regularize[SubstFor[Coth[v],u,x]/(1-x^2),x],x],x,Coth[v]]] /;
[all …]
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| H A D | HyperbolicTangentFunctions.m | 42 Int[Coth[a_.+b_.*x_],x_Symbol] :=
87 x - Coth[a+b*x]/b /;
403 Int[(A_.+B_.*Coth[c_.+d_.*x_])/(a_.+b_.*Coth[c_.+d_.*x_]),x_Symbol] :=
435 Int[(A_+B_.*Coth[c_.+d_.*x_])/Sqrt[a_.+b_.*Coth[c_.+d_.*x_]],x_Symbol] :=
472 Int[(A_.+B_.*Coth[c_.+d_.*x_])/Sqrt[a_.+b_.*Coth[c_.+d_.*x_]],x_Symbol] :=
473 Dist[(A+B)/2,Int[(1+Coth[c+d*x])/Sqrt[a+b*Coth[c+d*x]],x]] +
474 Dist[(A-B)/2,Int[(1-Coth[c+d*x])/Sqrt[a+b*Coth[c+d*x]],x]] /;
507 Int[(A_.+B_.*Coth[c_.+d_.*x_])*(a_+b_.*Coth[c_.+d_.*x_])^n_.,x_Symbol] :=
509 Int[(a*A+b*B+(b*A+a*B)*Coth[c+d*x])*(a+b*Coth[c+d*x])^(n-1),x] /;
542 Int[(A_.+B_.*Coth[c_.+d_.*x_])*(a_+b_.*Coth[c_.+d_.*x_])^n_,x_Symbol] :=
[all …]
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| H A D | TwoHyperbolicFunctions.m | 109 Cosh[a+b*x]^m*Coth[a+b*x]^(n-1)/(b*m) /;
192 Cosh[a+b*x]^m*Coth[a+b*x]^(n+1)/(b*m) +
268 Cosh[a+b*x]^m*Coth[a+b*x]^(n-1)/(b*m) +
499 Int[u_.*Cosh[v_]*Coth[w_]^n_.,x_Symbol] :=
500 Int[u*Sinh[v]*Coth[w]^(n-1),x] + Cosh[v-w]*Int[u*Csch[w]*Coth[w]^(n-1),x] /;
521 …Sinh[v] Coth[w]^n \[DifferentialD]x \[LongRightArrow] \[Integral]u Cosh[v] Coth[w]^(n-1) \[Diffe…
529 Int[u_.*Sinh[v_]*Coth[w_]^n_.,x_Symbol] :=
530 Int[u*Cosh[v]*Coth[w]^(n-1),x] + Sinh[v-w]*Int[u*Csch[w]*Coth[w]^(n-1),x] /;
1059 (*Basis: Csch[z]+Sinh[z]=Cosh[z] Coth[z]*)
1076 Int[(a*Cosh[c+d*x]*Coth[c+d*x])^n,x] /;
[all …]
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| /dports/math/reduce/Reduce-svn5758-src/contrib/rubi-red/rubi4/IntegrationRules/MathematicaNotebookFiles/HyperbolicFunctions/ |
| H A D | HyperbolicSubstitution.nb | 266 RowBox[{"Coth", "[",
318 RowBox[{"Coth", "[",
830 RowBox[{"Coth", "[",
847 RowBox[{"Coth", "[",
931 RowBox[{"Coth", "[",
1023 RowBox[{"Coth", "[",
1045 RowBox[{"Coth", "[",
1138 RowBox[{"Coth", "[",
1223 RowBox[{"Coth", "[",
1238 RowBox[{"Coth", "[",
[all …]
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| /dports/devel/pragmarcs/PragmARC-1378e7a/ |
| H A D | pragmarc-math-functions.adb | 119 function Coth (Angle : Real) return Real is subprogram
122 return Mth.Coth (Angle);
126 end Coth;
146 function Arccoth (Coth : Real) return Real is
149 return Mth.Arccoth (Coth);
|