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 CosIntegral

 http://functions.wolfram.com/06.38.21.0032.01

 Input Form

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

 Standard Form

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 MathML Form

 z 2 cos ( b z ) Ci ( a z ) z 1 2 b 3 ( ( - Ei ( - ( a - b ) z ) + Ci ( a z ) ( Γ ( 3 , - b z ) - Γ ( 3 , b z ) ) + 1 ( a - b ) 2 ( a + b ) 2 ( 2 ( a ( a - b ) ( a + b ) z sin ( a z ) - ( a 2 - 3 b 2 ) cos ( a z ) ) sin ( b z ) b 2 + 2 cos ( b z ) ( ( a - b ) ( a + b ) z cos ( a z ) b 2 + 2 a ( a 2 - 2 b 2 ) sin ( a z ) ) b + ( a 2 - b 2 ) 2 ( Ei ( ( a - b ) z ) + Ei ( - ( a + b ) z ) - Ei ( ( a + b ) z ) ) ) ) ) z z 2 b z CosIntegral a z 1 2 b 3 -1 -1 ExpIntegralEi -1 a -1 b z CosIntegral a z Gamma 3 -1 b z -1 Gamma 3 b z 1 a -1 b 2 a b 2 -1 2 a a -1 b a b z a z -1 a 2 -1 3 b 2 a z b z b 2 2 b z a -1 b a b z a z b 2 2 a a 2 -1 2 b 2 a z b a 2 -1 b 2 2 ExpIntegralEi a -1 b z ExpIntegralEi -1 a b z -1 ExpIntegralEi a b z [/itex]

 Rule Form

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

 2001-10-29