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 CosIntegral

 http://functions.wolfram.com/06.38.21.0068.01

 Input Form

 Integrate[z SinIntegral[b z] CosIntegral[a z], z] == (1/(8 a^2 b^2)) ((2 a^2 E^(I (a + b) z) CosIntegral[a z] (I (Gamma[2, (-I) b z] - Gamma[2, I b z]) + 2 b^2 z^2 SinIntegral[b z]) - I ((-a) b (-1 + E^(2 I a z)) (1 + E^(2 I b z)) + (a^2 + b^2) E^(I (a + b) z) (ExpIntegralEi[(-I) (a - b) z] - ExpIntegralEi[I (a - b) z] - ExpIntegralEi[(-I) (a + b) z] + ExpIntegralEi[I (a + b) z]) - 2 I b^2 E^(I (a + b) z) (Gamma[2, (-I) a z] + Gamma[2, I a z]) SinIntegral[b z]))/ E^(I (a + b) z))

 Standard Form

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 MathML Form

 z Si ( b z ) Ci ( a z ) z 1 8 a 2 b 2 ( - ( a + b ) z ( 2 a 2 ( a + b ) z Ci ( a z ) ( 2 b 2 Si ( b z ) z 2 + ( Γ ( 2 , - b z ) - Γ ( 2 , b z ) ) ) - ( - 2 ( a + b ) z ( Γ ( 2 , - a z ) + Γ ( 2 , a z ) ) Si ( b z ) b 2 - a ( - 1 + 2 a z ) ( 1 + 2 b z ) b + ( a 2 + b 2 ) ( a + b ) z ( Ei ( - ( a - b ) z ) - Ei ( ( a - b ) z ) - Ei ( - ( a + b ) z ) + Ei ( ( a + b ) z ) ) ) ) ) z z SinIntegral b z CosIntegral a z 1 8 a 2 b 2 -1 -1 a b z 2 a 2 a b z CosIntegral a z 2 b 2 SinIntegral b z z 2 Gamma 2 -1 b z -1 Gamma 2 b z -1 -2 a b z Gamma 2 -1 a z Gamma 2 a z SinIntegral b z b 2 -1 a -1 2 a z 1 2 b z b a 2 b 2 a b z ExpIntegralEi -1 a -1 b z -1 ExpIntegralEi a -1 b z -1 ExpIntegralEi -1 a b z ExpIntegralEi a b z [/itex]

 Rule Form

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

 2001-10-29