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 CosIntegral

 http://functions.wolfram.com/06.38.21.0039.01

 Input Form

 Integrate[z^3 Sinh[b z] CosIntegral[a z], z] == (1/(4 b^4)) (4 CosIntegral[a z] (b z (6 + b^2 z^2) Cosh[b z] - 3 (2 + b^2 z^2) Sinh[b z]) + (1/(a^2 + b^2)^3) (6 (a^2 + b^2)^3 (ExpIntegralEi[((-I) a + b) z] + ExpIntegralEi[(I a + b) z] - ExpIntegralEi[(-I) a z - b z] - ExpIntegralEi[I a z - b z]) + 4 b Sin[a z] ((-a) (2 (3 a^4 + 8 a^2 b^2 + 9 b^4) + b^2 (a^2 + b^2)^2 z^2) Cosh[b z] + a b (a^2 + b^2) (3 a^2 + 7 b^2) z Sinh[b z]) + 4 b^2 Cos[a z] (b (a^2 + b^2) (a^2 + 5 b^2) z Cosh[b z] - (3 a^4 + 6 a^2 b^2 + 11 b^4 + b^2 (a^2 + b^2)^2 z^2) Sinh[b z])))

 Standard Form

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 MathML Form

 z 3 sinh ( b z ) Ci ( a z ) z 1 4 b 4 ( 4 Ci ( a z ) ( b z ( b 2 z 2 + 6 ) cosh ( b z ) - 3 ( b 2 z 2 + 2 ) sinh ( b z ) ) + 1 ( a 2 + b 2 ) 3 ( 6 ( Ei ( ( b - a ) z ) + Ei ( ( b + a ) z ) - Ei ( - b z + a ( - ) z ) - Ei ( a z - b z ) ) ( a 2 + b 2 ) 3 + 4 b sin ( a z ) ( a b ( a 2 + b 2 ) ( 3 a 2 + 7 b 2 ) z sinh ( b z ) - a ( b 2 ( a 2 + b 2 ) 2 z 2 + 2 ( 3 a 4 + 8 b 2 a 2 + 9 b 4 ) ) cosh ( b z ) ) + 4 b 2 cos ( a z ) ( b ( a 2 + b 2 ) ( a 2 + 5 b 2 ) z cosh ( b z ) - ( 3 a 4 + 6 b 2 a 2 + 11 b 4 + b 2 ( a 2 + b 2 ) 2 z 2 ) sinh ( b z ) ) ) ) z z 3 b z CosIntegral a z 1 4 b 4 -1 4 CosIntegral a z b z b 2 z 2 6 b z -1 3 b 2 z 2 2 b z 1 a 2 b 2 3 -1 6 ExpIntegralEi b -1 a z ExpIntegralEi b a z -1 ExpIntegralEi -1 b z a -1 z -1 ExpIntegralEi a z -1 b z a 2 b 2 3 4 b a z a b a 2 b 2 3 a 2 7 b 2 z b z -1 a b 2 a 2 b 2 2 z 2 2 3 a 4 8 b 2 a 2 9 b 4 b z 4 b 2 a z b a 2 b 2 a 2 5 b 2 z b z -1 3 a 4 6 b 2 a 2 11 b 4 b 2 a 2 b 2 2 z 2 b z [/itex]

 Rule Form

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

 2001-10-29