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 SinhIntegral

 http://functions.wolfram.com/06.39.21.0028.01

 Input Form

 Integrate[z^2 Cos[b z] SinhIntegral[a z], z] == (1/(4 b^3)) (I ((1/(a^2 + b^2)^2) (2 (a^2 + b^2)^2 (ExpIntegralEi[(a - I b) z] - ExpIntegralEi[(-(a + I b)) z] - ExpIntegralEi[(a + I b) z] + ExpIntegralEi[(-a) z + I b z]) + 4 I b^2 Sin[b z] (a (a^2 + b^2) z Cosh[a z] + (a^2 + 3 b^2) Sinh[a z]) + 4 I Cos[b z] (2 a b (a^2 + 2 b^2) Cosh[a z] - b^3 (a^2 + b^2) z Sinh[a z])) + 2 (Gamma[3, (-I) b z] - Gamma[3, I b z]) SinhIntegral[a z]))

 Standard Form

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 MathML Form

 z 2 cos ( b z ) Shi ( a z ) z 1 4 b 3 ( ( 1 ( a 2 + b 2 ) 2 ( 4 sin ( b z ) ( a ( a 2 + b 2 ) z cosh ( a z ) + ( a 2 + 3 b 2 ) sinh ( a z ) ) b 2 + 2 ( a 2 + b 2 ) 2 ( - Ei ( - ( a + b ) z ) - Ei ( ( a + b ) z ) + Ei ( ( a - b ) z ) + Ei ( b z - a z ) ) + 4 cos ( b z ) ( 2 a b ( a 2 + 2 b 2 ) cosh ( a z ) - b 3 ( a 2 + b 2 ) z sinh ( a z ) ) ) + 2 ( Γ ( 3 , - b z ) - Γ ( 3 , b z ) ) Shi ( a z ) ) ) z z 2 b z SinhIntegral a z 1 4 b 3 -1 1 a 2 b 2 2 -1 4 b z a a 2 b 2 z a z a 2 3 b 2 a z b 2 2 a 2 b 2 2 -1 ExpIntegralEi -1 a b z -1 ExpIntegralEi a b z ExpIntegralEi a -1 b z ExpIntegralEi b z -1 a z 4 b z 2 a b a 2 2 b 2 a z -1 b 3 a 2 b 2 z a z 2 Gamma 3 -1 b z -1 Gamma 3 b z SinhIntegral a z [/itex]

 Rule Form

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

 2001-10-29