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 CosIntegral

 http://functions.wolfram.com/06.38.21.0038.01

 Input Form

 Integrate[z^2 Sinh[b z] CosIntegral[a z], z] == (1/(4 b^3)) (4 CosIntegral[a z] ((2 + b^2 z^2) Cosh[b z] - 2 b z Sinh[b z]) + (1/(a^2 + b^2)^2) (-2 (a^2 + b^2)^2 (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) b (a^2 + b^2) z Cosh[b z] + 2 a (a^2 + 2 b^2) Sinh[b z]) + 4 b^2 Cos[a z] ((a^2 + 3 b^2) Cosh[b z] - b (a^2 + b^2) z Sinh[b z])))

 Standard Form

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 MathML Form

 z 2 sinh ( b z ) Ci ( a z ) z 1 4 b 3 ( 4 Ci ( a z ) ( ( b 2 z 2 + 2 ) cosh ( b z ) - 2 b z sinh ( b z ) ) + 1 ( a 2 + b 2 ) 2 ( 4 cos ( a z ) ( ( a 2 + 3 b 2 ) cosh ( b z ) - b ( a 2 + b 2 ) z sinh ( b z ) ) b 2 + 4 sin ( a z ) ( 2 a ( a 2 + 2 b 2 ) sinh ( b z ) - a b ( a 2 + b 2 ) z cosh ( b z ) ) b - 2 ( a 2 + b 2 ) 2 ( Ei ( ( b - a ) z ) + Ei ( ( b + a ) z ) + Ei ( - b z + a ( - ) z ) + Ei ( a z - b z ) ) ) ) z z 2 b z CosIntegral a z 1 4 b 3 -1 4 CosIntegral a z b 2 z 2 2 b z -1 2 b z b z 1 a 2 b 2 2 -1 4 a z a 2 3 b 2 b z -1 b a 2 b 2 z b z b 2 4 a z 2 a a 2 2 b 2 b z -1 a b a 2 b 2 z b z b -1 2 a 2 b 2 2 ExpIntegralEi b -1 a z ExpIntegralEi b a z ExpIntegralEi -1 b z a -1 z ExpIntegralEi a z -1 b z [/itex]

 Rule Form

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

 2001-10-29