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 SinhIntegral

 http://functions.wolfram.com/06.39.21.0069.01

 Input Form

 Integrate[z SinIntegral[b z] SinhIntegral[a z], z] == (-(1/(8 a^2 b^2))) (a b E^((a - I b) z) + (a b)/E^((a + I b) z) + a b E^((a + I b) z) + a b E^((-a) z + I b z) - I a^2 ExpIntegralEi[(a - I b) z] + I b^2 ExpIntegralEi[(a - I b) z] + I a^2 ExpIntegralEi[(-(a + I b)) z] - I b^2 ExpIntegralEi[(-(a + I b)) z] + I a^2 ExpIntegralEi[(a + I b) z] - I b^2 ExpIntegralEi[(a + I b) z] - I a^2 ExpIntegralEi[(-a) z + I b z] + I b^2 ExpIntegralEi[(-a) z + I b z] + 2 b^2 (-Gamma[2, (-a) z] + Gamma[2, a z]) SinIntegral[b z] - 2 I a^2 SinhIntegral[a z] (Gamma[2, (-I) b z] - Gamma[2, I b z] - 2 I b^2 z^2 SinIntegral[b z]))

 Standard Form

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 MathML Form

 z Si ( b z ) Shi ( a z ) z - 1 8 a 2 b 2 ( Ei ( - ( a + b ) z ) a 2 + Ei ( ( a + b ) z ) a 2 - Ei ( ( a - b ) z ) a 2 - Ei ( b z - a z ) a 2 - 2 Shi ( a z ) ( - 2 b 2 Si ( b z ) z 2 + Γ ( 2 , - b z ) - Γ ( 2 , b z ) ) a 2 + b - ( a + b ) z a + b ( a + b ) z a + b ( a - b ) z a + b b z - a z a - b 2 Ei ( - ( a + b ) z ) - b 2 Ei ( ( a + b ) z ) + b 2 Ei ( ( a - b ) z ) + b 2 Ei ( b z - a z ) + 2 b 2 ( Γ ( 2 , a z ) - Γ ( 2 , - a z ) ) Si ( b z ) ) z z SinIntegral b z SinhIntegral a z -1 1 8 a 2 b 2 -1 ExpIntegralEi -1 a b z a 2 ExpIntegralEi a b z a 2 -1 ExpIntegralEi a -1 b z a 2 -1 ExpIntegralEi b z -1 a z a 2 -1 2 SinhIntegral a z -2 b 2 SinIntegral b z z 2 Gamma 2 -1 b z -1 Gamma 2 b z a 2 b -1 a b z a b a b z a b a -1 b z a b b z -1 a z a -1 b 2 ExpIntegralEi -1 a b z -1 b 2 ExpIntegralEi a b z b 2 ExpIntegralEi a -1 b z b 2 ExpIntegralEi b z -1 a z 2 b 2 Gamma 2 a z -1 Gamma 2 -1 a z SinIntegral b z [/itex]

 Rule Form

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

 2001-10-29