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 CosIntegral

 http://functions.wolfram.com/06.38.21.0033.01

 Input Form

 Integrate[z^3 Cos[b z] CosIntegral[a z], z] == (1/(4 b^4)) (-2 CosIntegral[a z] (Gamma[4, (-I) b z] + Gamma[4, I b z]) + (1/((a - b)^3 (a + b)^3)) (6 (a^2 - b^2)^3 (ExpIntegralEi[(-I) (a - b) z] + ExpIntegralEi[I (a - b) z] + ExpIntegralEi[(-I) (a + b) z] + ExpIntegralEi[I (a + b) z]) + 4 b^2 Cos[b z] ((-(-3 a^4 + 6 a^2 b^2 - 11 b^4 + b^2 (a^2 - b^2)^2 z^2)) Cos[a z] + a (-3 a^4 + 10 a^2 b^2 - 7 b^4) z Sin[a z]) + 4 b (b^2 (a^4 - 6 a^2 b^2 + 5 b^4) z Cos[a z] - a (-2 (3 a^4 - 8 a^2 b^2 + 9 b^4) + b^2 (a^2 - b^2)^2 z^2) Sin[a z]) Sin[b z]))

 Standard Form

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 MathML Form

 z 3 cos ( b z ) Ci ( a z ) z 1 4 b 4 ( 1 ( a - b ) 3 ( a + b ) 3 ( 6 ( Ei ( - ( a - b ) z ) + Ei ( ( a - b ) z ) + Ei ( - ( a + b ) z ) + Ei ( ( a + b ) z ) ) ( a 2 - b 2 ) 3 + 4 b 2 cos ( b z ) ( a ( - 3 a 4 + 10 b 2 a 2 - 7 b 4 ) z sin ( a z ) - ( - 3 a 4 + 6 b 2 a 2 - 11 b 4 + b 2 ( a 2 - b 2 ) 2 z 2 ) cos ( a z ) ) + 4 b ( b 2 ( a 4 - 6 b 2 a 2 + 5 b 4 ) z cos ( a z ) - a ( b 2 ( a 2 - b 2 ) 2 z 2 - 2 ( 3 a 4 - 8 b 2 a 2 + 9 b 4 ) ) sin ( a z ) ) sin ( b z ) ) - 2 Ci ( a z ) ( Γ ( 4 , - b z ) + Γ ( 4 , b z ) ) ) z z 3 b z CosIntegral a z 1 4 b 4 -1 1 a -1 b 3 a b 3 -1 6 ExpIntegralEi -1 a -1 b z ExpIntegralEi a -1 b z ExpIntegralEi -1 a b z ExpIntegralEi a b z a 2 -1 b 2 3 4 b 2 b z a -3 a 4 10 b 2 a 2 -1 7 b 4 z a z -1 -3 a 4 6 b 2 a 2 -1 11 b 4 b 2 a 2 -1 b 2 2 z 2 a z 4 b b 2 a 4 -1 6 b 2 a 2 5 b 4 z a z -1 a b 2 a 2 -1 b 2 2 z 2 -1 2 3 a 4 -1 8 b 2 a 2 9 b 4 a z b z -1 2 CosIntegral a z Gamma 4 -1 b z Gamma 4 b z [/itex]

 Rule Form

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

 2001-10-29