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 SinIntegral

 http://functions.wolfram.com/06.37.21.0033.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2001-10-29