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 SinhIntegral

 http://functions.wolfram.com/06.39.21.0073.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2001-10-29