tests4/SpecialFunctions/HyperbolicIntegralFunctions.m

17 … 6, -((3*x*Cosh[b*x])/(2*b^3)) - (x^3*Cosh[b*x])/(4*b) + (3*Sinh[b*x])/(2*b^4) + (3*x^2*Sinh[b*x])…
18 {x^2*SinhIntegral[b*x], x, 5, -((2*Cosh[b*x])/(3*b^3)) - (x^2*Cosh[b*x])/(3*b) + (2*x*Sinh[b*x])/(3…
19 {x^1*SinhIntegral[b*x], x, 4, -((x*Cosh[b*x])/(2*b)) + Sinh[b*x]/(2*b^2) + (1/2)*x^2*SinhIntegral[b…
22 {SinhIntegral[b*x]/x^2, x, 4, b*CoshIntegral[b*x] - Sinh[b*x]/x - SinhIntegral[b*x]/x}
23 {SinhIntegral[b*x]/x^3, x, 5, -((b*Cosh[b*x])/(4*x)) - Sinh[b*x]/(4*x^2) + (1/4)*b^2*SinhIntegral[b…
28 …Sinh[b*x])/b^3 + (2*Sinh[b*x]^2)/b^4 + (x^2*Sinh[b*x]^2)/(4*b^2) - (3*x*Cosh[b*x]*SinhIntegral[b*x…
29 …b*x]*Sinh[b*x])/(6*b^3) + (x*Sinh[b*x]^2)/(3*b^2) - (4*Cosh[b*x]*SinhIntegral[b*x])/(3*b^3) - (2*x…
30 …hIntegral[2*b*x]/(2*b^2)) + Log[x]/(2*b^2) + Sinh[b*x]^2/(2*b^2) - (x*Cosh[b*x]*SinhIntegral[b*x])…
41 …m)))) - (x^m*Gamma[1 + m, b*x])/(E^a*(b*x)^m*(2*b*(1 + m))) + (a*Int[(x^m*Sinh[a + b*x])/(a + b*x)…
43 …3*Cosh[a + b*x])/(4*b) + (3*Sinh[a + b*x])/(2*b^4) + (a^2*Sinh[a + b*x])/(4*b^4) - (a*x*Sinh[a + b…
44 …*x*Cosh[a + b*x])/(3*b^2) - (x^2*Cosh[a + b*x])/(3*b) - (a*Sinh[a + b*x])/(3*b^3) + (2*x*Sinh[a + …
45 {x^1*SinhIntegral[a + b*x], x, 7, (a*Cosh[a + b*x])/(2*b^2) - (x*Cosh[a + b*x])/(2*b) + Sinh[a + b*…
48 {SinhIntegral[a + b*x]/x^2, x, 7, (b*CoshIntegral[b*x]*Sinh[a])/a + (b*Cosh[a]*SinhIntegral[b*x])/a…
49 …) - (b^2*CoshIntegral[b*x]*Sinh[a])/(2*a^2) - (b*Sinh[a + b*x])/(2*a*x) - (b^2*Cosh[a]*SinhIntegra…
54 …Sinh[a + b*x])/(4*b^4) - (3*x*Cosh[a + b*x]*Sinh[a + b*x])/(4*b^3) + (3*Sinh[a + b*x]^2)/(8*b^4) +…
55 …Sinh[a + b*x])/(3*b^3) - Sinh[2*a + 2*b*x]/(12*b^3) - (4*Cosh[a + b*x]*SinhIntegral[a + b*x])/(3*b…
56 …SinhIntegral[a + b*x])/b^2 - (x*Cosh[a + b*x]*SinhIntegral[a + b*x])/b + (Sinh[a + b*x]*SinhIntegr…
67 …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 -…
69 {Sinh[b*x]*SinhIntegral[b*x]/x, x, 1, (1/2)*SinhIntegral[b*x]^2}
70 {Sinh[b*x]*SinhIntegral[b*x], x, 5, (Cosh[b*x]*SinhIntegral[b*x])/b - SinhIntegral[2*b*x]/(2*b)}
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…
76 …*SinhIntegral[b*x])/x, x] - (b*Sinh[b*x]^2)/(2*x) - Sinh[2*b*x]/(8*x^2) - (Cosh[b*x]*SinhIntegral[…
77 {Cosh[b*x]*SinhIntegral[b*x]/x^2, x, 7, b*CoshIntegral[2*b*x] - Sinh[2*b*x]/(2*x) - (Cosh[b*x]*Sinh…
79 {Cosh[b*x]*SinhIntegral[b*x], x, 5, -(CoshIntegral[2*b*x]/(2*b)) + Log[x]/(2*b) + (Sinh[b*x]*SinhIn…
80 …nhIntegral[b*x], x, 8, x/(2*b) - (Cosh[b*x]*Sinh[b*x])/(2*b^2) - (Cosh[b*x]*SinhIntegral[b*x])/b^2…
81 …osh[b*x]*Sinh[b*x])/(2*b^2) + (5*Sinh[b*x]^2)/(4*b^3) - (2*x*Cosh[b*x]*SinhIntegral[b*x])/b^2 + (2…
82 …Sinh[b*x])/b^4 - (x^2*Cosh[b*x]*Sinh[b*x])/(2*b^2) + (2*x*Sinh[b*x]^2)/b^3 - (6*Cosh[b*x]*SinhInte…
89 (* {Sinh[a + b*x]*SinhIntegral[c + d*x]/x^3, x, 0, 0} *)
90 …Sinh[a + b*x]*SinhIntegral[c + d*x]/x^2, x, 19, -((d*Cosh[a - c]*CoshIntegral[(b - d)*x])/(2*c)) +…
91 {Sinh[a + b*x]*SinhIntegral[c + d*x]/x, x, 0, Int[(Sinh[a + b*x]*SinhIntegral[c + d*x])/x, x]}
92 …Sinh[a + b*x]*SinhIntegral[c + d*x], x, 9, (CoshIntegral[(c*(b - d))/d + (b - d)*x]*Sinh[a - (b*c)…
93 …Sinh[a + b*x]*SinhIntegral[c + d*x], x, 24, Cosh[a - c + (b - d)*x]/(2*b*(b - d)) - Cosh[a + c + (…
94 …Sinh[a + b*x]*SinhIntegral[c + d*x], x, 46, -((c*Cosh[a - c + (b - d)*x])/(2*b*(b - d)*d)) + (x*Co…
95 (* {x^3*Sinh[a + b*x]*SinhIntegral[c + d*x], x, 0, 0} *)
99 …Sinh[a + b*x]*SinhIntegral[c + d*x])/x, x] - (d*CoshIntegral[(b - d)*x]*Sinh[a - c])/(2*c) + (d*Co…
101 … + d)*x])/(2*b) + (Sinh[a - (b*c)/d]*SinhIntegral[(c*(b - d))/d + (b - d)*x])/(2*b) + (Sinh[a + b*…
102 …Sinh[a - (b*c)/d])/(2*b^2) + (CoshIntegral[(c*(b + d))/d + (b + d)*x]*Sinh[a - (b*c)/d])/(2*b^2) +…
103 …Sinh[a - (b*c)/d]))/(2*b^3*d^2) - (CoshIntegral[((b + d)*(c + d*x))/d]*((b^2*c^2 + 2*d^2)*Cosh[a -…
117 …*x^2*Cosh[b*x])/(4*b^2) + (1/4)*x^4*CoshIntegral[b*x] - (3*x*Sinh[b*x])/(2*b^3) - (x^3*Sinh[b*x])/…
118 …, (2*x*Cosh[b*x])/(3*b^2) + (1/3)*x^3*CoshIntegral[b*x] - (2*Sinh[b*x])/(3*b^3) - (x^2*Sinh[b*x])/…
119 {x^1*CoshIntegral[b*x], x, 4, Cosh[b*x]/(2*b^2) + (1/2)*x^2*CoshIntegral[b*x] - (x*Sinh[b*x])/(2*b)}
120 {x^0*CoshIntegral[b*x], x, 1, x*CoshIntegral[b*x] - Sinh[b*x]/b}
123 …Cosh[b*x]/(4*x^2)) + (1/4)*b^2*CoshIntegral[b*x] - CoshIntegral[b*x]/(2*x^2) - (b*Sinh[b*x])/(4*x)}
128 …osh[b*x]*Sinh[b*x])/b^3 - (3*x*CoshIntegral[b*x]*Sinh[b*x])/b^3 - (x^3*CoshIntegral[b*x]*Sinh[b*x]…
129 …]^2 - (5*Cosh[b*x]*Sinh[b*x])/(6*b^3) - (4*CoshIntegral[b*x]*Sinh[b*x])/(3*b^3) - (2*x^2*CoshInteg…
130 …oshIntegral[2*b*x]/(2*b^2) - Log[x]/(2*b^2) - (x*CoshIntegral[b*x]*Sinh[b*x])/b + Sinh[b*x]^2/(2*b…
131 {x^0*CoshIntegral[b*x]^2, x, 6, x*CoshIntegral[b*x]^2 - (2*CoshIntegral[b*x]*Sinh[b*x])/b + SinhInt…
143 …Sinh[a + b*x])/(2*b^4) + (a^3*Sinh[a + b*x])/(4*b^4) - (3*x*Sinh[a + b*x])/(2*b^3) - (a^2*x*Sinh[a…
144 …3*CoshIntegral[a + b*x] - (2*Sinh[a + b*x])/(3*b^3) - (a^2*Sinh[a + b*x])/(3*b^3) + (a*x*Sinh[a + …
145 …al[a + b*x])/(2*b^2) + (1/2)*x^2*CoshIntegral[a + b*x] + (a*Sinh[a + b*x])/(2*b^2) - (x*Sinh[a + b…
146 {x^0*CoshIntegral[a + b*x], x, 1, ((a + b*x)*CoshIntegral[a + b*x])/b - Sinh[a + b*x]/b}
148 …gral[b*x])/a - (b*CoshIntegral[a + b*x])/a - CoshIntegral[a + b*x]/x + (b*Sinh[a]*SinhIntegral[b*x…
149 …[a + b*x]/(2*x^2) + (b^2*CoshIntegral[b*x]*Sinh[a])/(2*a) + (b^2*Cosh[a]*SinhIntegral[b*x])/(2*a) …
154 …Sinh[a + b*x])/(4*b^4) - (3*x*Cosh[a + b*x]*Sinh[a + b*x])/(4*b^3) + (CoshIntegral[a + b*x]*((6 + …
155 …Sinh[a + b*x])/(3*b^3) - (4*CoshIntegral[a + b*x]*Sinh[a + b*x])/(3*b^3) - (2*a^2*CoshIntegral[a +…
156 … - Log[a + b*x]/(2*b^2) + (a*CoshIntegral[a + b*x]*Sinh[a + b*x])/b^2 - (x*CoshIntegral[a + b*x]*S…
157 …2, x, 5, ((a + b*x)*CoshIntegral[a + b*x]^2)/b - (2*CoshIntegral[a + b*x]*Sinh[a + b*x])/b + SinhI…
167 …2 + b^2*CoshIntegral[2*b*x] - (b*Cosh[b*x]*Sinh[b*x])/(2*x) - (b*CoshIntegral[b*x]*Sinh[b*x])/(2*x…
168 …sh[b*x]^2/x) - (Cosh[b*x]*CoshIntegral[b*x])/x + b*Int[(CoshIntegral[b*x]*Sinh[b*x])/x, x] + b*Sin…
170 {Cosh[b*x]*CoshIntegral[b*x], x, 5, (CoshIntegral[b*x]*Sinh[b*x])/b - SinhIntegral[2*b*x]/(2*b)}
171 …oshIntegral[2*b*x]/(2*b^2) + Log[x]/(2*b^2) + (x*CoshIntegral[b*x]*Sinh[b*x])/b - Sinh[b*x]^2/(2*b…
172 …*x])/b^2 + (5*Cosh[b*x]*Sinh[b*x])/(4*b^3) + (2*CoshIntegral[b*x]*Sinh[b*x])/b^3 + (x^2*CoshIntegr…
173 …*Cosh[b*x]*Sinh[b*x])/b^3 + (6*x*CoshIntegral[b*x]*Sinh[b*x])/b^3 + (x^3*CoshIntegral[b*x]*Sinh[b*…
176 …Sinh[b*x]*CoshIntegral[b*x]/x^3, x, 12, -((b*Cosh[b*x]^2)/(2*x)) - (b*Cosh[2*b*x])/(4*x) - (b*Cosh…
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]}
179 {Sinh[b*x]*CoshIntegral[b*x], x, 5, (Cosh[b*x]*CoshIntegral[b*x])/b - CoshIntegral[2*b*x]/(2*b) - L…
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…
181 …Sinh[b*x]*CoshIntegral[b*x], x, 12, -(x^2/(4*b)) + Cosh[b*x]^2/(4*b^3) + (2*Cosh[b*x]*CoshIntegral…
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*…
189 {Cosh[5*x]*CoshIntegral[2*x], x, 6, (1/5)*CoshIntegral[2*x]*Sinh[5*x] - (1/10)*SinhIntegral[3*x] - …
192 (* {Sinh[a + b*x]*CoshIntegral[c + d*x]/x^3, x, 0, 0} *)
193 …Sinh[a + b*x]*CoshIntegral[c + d*x]/x^2, x, 19, b*Int[(Cosh[a + b*x]*CoshIntegral[c + d*x])/x, x] …
194 {Sinh[a + b*x]*CoshIntegral[c + d*x]/x, x, 0, Int[(CoshIntegral[c + d*x]*Sinh[a + b*x])/x, x]}
195 …Sinh[a + b*x]*CoshIntegral[c + d*x], x, 9, -((Cosh[a - (b*c)/d]*CoshIntegral[(c*(b - d))/d + (b - …
196 …Sinh[a + b*x]*CoshIntegral[c + d*x], x, 24, (c*Cosh[a - (b*c)/d]*CoshIntegral[(c*(b - d))/d + (b -…
197 …Sinh[a + b*x]*CoshIntegral[c + d*x], x, 46, Cosh[a - c + (b - d)*x]/(2*b*(b - d)^2) + Cosh[a - c +…
198 (* {x^3*Sinh[a + b*x]*CoshIntegral[c + d*x], x, 0, 0} *)
202 …Sinh[a + b*x])/x, x] + (d*Sinh[a - c]*SinhIntegral[(b - d)*x])/(2*c) + (d*Sinh[a + c]*SinhIntegral…
204 …d + (b - d)*x]*Sinh[a - (b*c)/d])/(2*b)) - (CoshIntegral[(c*(b + d))/d + (b + d)*x]*Sinh[a - (b*c)…
205 …Sinh[a - (b*c)/d])/(2*b*d) + (c*CoshIntegral[(c*(b + d))/d + (b + d)*x]*Sinh[a - (b*c)/d])/(2*b*d)…
206 …Sinh[a - (b*c)/d]))/(2*b^3*d^2) - (CoshIntegral[((b + d)*(c + d*x))/d]*(2*b*c*d*Cosh[a - (b*c)/d] …