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 SinIntegral

 http://functions.wolfram.com/06.37.21.0039.01

 Input Form

 Integrate[z^3 Sinh[b z] SinIntegral[a z], z] == (-(1/(4 b^4))) (I ((1/(a^2 + b^2)^3) (-6 (a^2 + b^2)^3 (ExpIntegralEi[((-I) a + b) z] - ExpIntegralEi[(I a + b) z] - ExpIntegralEi[(-I) a z - b z] + ExpIntegralEi[I a z - b z]) + 4 I b 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) Cosh[b z] - a b (a^2 + b^2) (3 a^2 + 7 b^2) z Sinh[b z]) + 4 I b^2 Sin[a z] (b (a^2 + b^2) (a^2 + 5 b^2) z Cosh[b z] - (3 a^4 + 6 a^2 b^2 + 11 b^4 + b^2 (a^2 + b^2)^2 z^2) Sinh[b z])) - 2 I (Gamma[4, (-b) z] - Gamma[4, b z]) SinIntegral[a z]))

 Standard Form

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 MathML Form

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

 Rule Form

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

 2001-10-29