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 SinhIntegral

 http://functions.wolfram.com/06.39.21.0057.01

 Input Form

 Integrate[z^3 SinhIntegral[a z] SinhIntegral[b z], z] == (1/8) ((2 (3 (a^2 - b^2)^2 (a^4 + b^4) CoshIntegral[(a - b) z] - 3 (a^2 - b^2)^2 (a^4 + b^4) CoshIntegral[(a + b) z] + a b (a b Sinh[a z] (b (a^4 + 2 a^2 b^2 - 3 b^4) z Cosh[b z] + (-3 a^4 + 14 a^2 b^2 - 3 b^4) Sinh[b z]) + Cosh[a z] ((6 b^6 + a^2 b^4 (-10 + b^2 z^2) - 2 a^4 b^2 (5 + b^2 z^2) + a^6 (6 + b^2 z^2)) Cosh[b z] + a^2 b (-3 a^4 + 2 a^2 b^2 + b^4) z Sinh[b z]))))/ (a^4 (a - b)^2 b^4 (a + b)^2) - (1/b^4) (2 (b z (6 + b^2 z^2) Cosh[b z] - 3 (2 + b^2 z^2) Sinh[b z]) SinhIntegral[a z]) + (1/a^4) (2 ((-a) z (6 + a^2 z^2) Cosh[a z] + 3 (2 + a^2 z^2) Sinh[a z] + a^4 z^4 SinhIntegral[a z]) SinhIntegral[b z]))

 Standard Form

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 MathML Form

 z 3 Shi ( a z ) Shi ( b z ) z 1 8 ( ( 2 ( 3 ( a 4 + b 4 ) Chi ( ( a - b ) z ) ( a 2 - b 2 ) 2 - 3 ( a 4 + b 4 ) Chi ( ( a + b ) z ) ( a 2 - b 2 ) 2 + a b ( a b sinh ( a z ) ( b ( a 4 + 2 b 2 a 2 - 3 b 4 ) z cosh ( b z ) + ( - 3 a 4 + 14 b 2 a 2 - 3 b 4 ) sinh ( b z ) ) + cosh ( a z ) ( b ( - 3 a 4 + 2 b 2 a 2 + b 4 ) z sinh ( b z ) a 2 + ( ( b 2 z 2 + 6 ) a 6 - 2 b 2 ( b 2 z 2 + 5 ) a 4 + b 4 ( b 2 z 2 - 10 ) a 2 + 6 b 6 ) cosh ( b z ) ) ) ) ) / ( a 4 ( a - b ) 2 b 4 ( a + b ) 2 ) - 1 b 4 ( 2 ( b z ( b 2 z 2 + 6 ) cosh ( b z ) - 3 ( b 2 z 2 + 2 ) sinh ( b z ) ) Shi ( a z ) ) + 1 a 4 ( 2 ( a 4 Shi ( a z ) z 4 - a ( a 2 z 2 + 6 ) cosh ( a z ) z + 3 ( a 2 z 2 + 2 ) sinh ( a z ) ) Shi ( b z ) ) ) z z 3 SinhIntegral a z SinhIntegral b z 1 8 2 3 a 4 b 4 CoshIntegral a -1 b z a 2 -1 b 2 2 -1 3 a 4 b 4 CoshIntegral a b z a 2 -1 b 2 2 a b a b a z b a 4 2 b 2 a 2 -1 3 b 4 z b z -3 a 4 14 b 2 a 2 -1 3 b 4 b z a z b -3 a 4 2 b 2 a 2 b 4 z b z a 2 b 2 z 2 6 a 6 -1 2 b 2 b 2 z 2 5 a 4 b 4 b 2 z 2 -10 a 2 6 b 6 b z a 4 a -1 b 2 b 4 a b 2 -1 -1 1 b 4 -1 2 b z b 2 z 2 6 b z -1 3 b 2 z 2 2 b z SinhIntegral a z 1 a 4 -1 2 a 4 SinhIntegral a z z 4 -1 a a 2 z 2 6 a z z 3 a 2 z 2 2 a z SinhIntegral b z [/itex]

 Rule Form

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 Date Added to functions.wolfram.com (modification date)

 2001-10-29