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 SinhIntegral

 http://functions.wolfram.com/06.39.21.0056.01

 Input Form

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

 Standard Form

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 MathML Form

 z 2 Shi ( a z ) Shi ( b z ) z 1 6 ( - 2 ( ( b 2 z 2 + 2 ) cosh ( b z ) - 2 b z sinh ( b z ) ) Shi ( a z ) b 3 + 1 a 3 ( 2 ( a 3 Shi ( a z ) z 3 + 2 a sinh ( a z ) z - ( a 2 z 2 + 2 ) cosh ( a z ) ) Shi ( b z ) ) + 1 a 3 ( a - b ) b 3 ( a + b ) ( 2 ( a b ( b ( a 2 + 2 b 2 ) cosh ( b z ) sinh ( a z ) + a cosh ( a z ) ( b ( a 2 - b 2 ) z cosh ( b z ) - ( 2 a 2 + b 2 ) sinh ( b z ) ) ) + ( a 5 - b 2 a 3 - b 3 a 2 + b 5 ) Shi ( ( a - b ) z ) + ( a 5 - b 2 a 3 + b 3 a 2 - b 5 ) Shi ( ( a + b ) z ) ) ) ) z z 2 SinhIntegral a z SinhIntegral b z 1 6 -1 2 b 2 z 2 2 b z -1 2 b z b z SinhIntegral a z b 3 -1 1 a 3 -1 2 a 3 SinhIntegral a z z 3 2 a a z z -1 a 2 z 2 2 a z SinhIntegral b z 1 a 3 a -1 b b 3 a b -1 2 a b b a 2 2 b 2 b z a z a a z b a 2 -1 b 2 z b z -1 2 a 2 b 2 b z a 5 -1 b 2 a 3 -1 b 3 a 2 b 5 SinhIntegral a -1 b z a 5 -1 b 2 a 3 b 3 a 2 -1 b 5 SinhIntegral a b z [/itex]

 Rule Form

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

 2001-10-29