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 ExpIntegralEi

 http://functions.wolfram.com/06.35.21.0045.01

 Input Form

 Integrate[z^3 Sinh[b z] ExpIntegralEi[a z], z] == (1/b^4) (ExpIntegralEi[a z] (b z (6 + b^2 z^2) Cosh[b z] - 3 (2 + b^2 z^2) Sinh[b z]) + (1/((a - b)^3 (a + b)^3)) ((-b) E^(a z) (2 a (3 a^4 - 8 a^2 b^2 + 9 b^4) + b^2 (a^4 - 6 a^2 b^2 + 5 b^4) z + a b^2 (a^2 - b^2)^2 z^2) Cosh[b z] + 3 (-a^2 + b^2)^3 (ExpIntegralEi[(a - b) z] - ExpIntegralEi[(a + b) z]) + b^2 E^(a z) (3 a^4 - 6 a^2 b^2 + 11 b^4 + a (3 a^4 - 10 a^2 b^2 + 7 b^4) z + b^2 (a^2 - b^2)^2 z^2) Sinh[b z]))

 Standard Form

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 MathML Form

 z 3 sinh ( b z ) Ei ( a z ) z 1 b 4 ( 1 ( a - b ) 3 ( a + b ) 3 ( 3 ( Ei ( ( a - b ) z ) - Ei ( ( a + b ) z ) ) ( b 2 - a 2 ) 3 - b a z ( a ( a 2 - b 2 ) 2 z 2 b 2 + ( a 4 - 6 b 2 a 2 + 5 b 4 ) z b 2 + 2 a ( 3 a 4 - 8 b 2 a 2 + 9 b 4 ) ) cosh ( b z ) + b 2 a z ( 3 a 4 - 6 b 2 a 2 + ( 3 a 4 - 10 b 2 a 2 + 7 b 4 ) z a + 11 b 4 + b 2 ( a 2 - b 2 ) 2 z 2 ) sinh ( b z ) ) + Ei ( a z ) ( b z ( b 2 z 2 + 6 ) cosh ( b z ) - 3 ( b 2 z 2 + 2 ) sinh ( b z ) ) ) z z 3 b z ExpIntegralEi a z 1 b 4 -1 1 a -1 b 3 a b 3 -1 3 ExpIntegralEi a -1 b z -1 ExpIntegralEi a b z b 2 -1 a 2 3 -1 b a z a a 2 -1 b 2 2 z 2 b 2 a 4 -1 6 b 2 a 2 5 b 4 z b 2 2 a 3 a 4 -1 8 b 2 a 2 9 b 4 b z b 2 a z 3 a 4 -1 6 b 2 a 2 3 a 4 -1 10 b 2 a 2 7 b 4 z a 11 b 4 b 2 a 2 -1 b 2 2 z 2 b z ExpIntegralEi a z b z b 2 z 2 6 b z -1 3 b 2 z 2 2 b z [/itex]

 Rule Form

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

 2001-10-29