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 ExpIntegralEi

 http://functions.wolfram.com/06.35.21.0036.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2001-10-29