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 SinhIntegral

 http://functions.wolfram.com/06.39.21.0067.01

 Input Form

 Integrate[z^3 ExpIntegralEi[b z] SinhIntegral[a z], z] == (1/4) ((1/b^4) (3 (ExpIntegralEi[(-a + b) z] - ExpIntegralEi[(a + b) z])) - (1/(2 b^3)) ((6 E^((-a + b) z))/(-a + b) - (6 E^((a + b) z))/(a + b) + (3 b Gamma[2, (a - b) z])/(a - b)^2 - (3 b Gamma[2, (-(a + b)) z])/ (a + b)^2 + (b^2 Gamma[3, (a - b) z])/(-a + b)^3 - (b^2 Gamma[3, (-(a + b)) z])/(a + b)^3) - (1/(2 a^4)) ((6 a E^((-a + b) z))/(a - b) - (6 a E^((a + b) z))/(a + b) - 6 ExpIntegralEi[(-a + b) z] + 6 ExpIntegralEi[(a + b) z] + (3 a^2 Gamma[2, (a - b) z])/(a - b)^2 - (3 a^2 Gamma[2, (-(a + b)) z])/ (a + b)^2 + (a^3 Gamma[3, (a - b) z])/(a - b)^3 - (a^3 Gamma[3, (-(a + b)) z])/(a + b)^3 - ExpIntegralEi[b z] Gamma[4, (-a) z] + ExpIntegralEi[b z] Gamma[4, a z]) + (z^4 ExpIntegralEi[b z] + Gamma[4, (-b) z]/b^4) SinhIntegral[a z])

 Standard Form

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 MathML Form

 z 3 Ei ( b z ) Shi ( a z ) z 1 4 ( - 1 2 b 3 ( Γ ( 3 , ( a - b ) z ) b 2 ( b - a ) 3 - Γ ( 3 , - ( a + b ) z ) b 2 ( a + b ) 3 + 3 Γ ( 2 , ( a - b ) z ) b ( a - b ) 2 - 3 Γ ( 2 , - ( a + b ) z ) b ( a + b ) 2 + 6 ( b - a ) z b - a - 6 ( a + b ) z a + b ) + 3 ( Ei ( ( b - a ) z ) - Ei ( ( a + b ) z ) ) b 4 - 1 2 a 4 ( Γ ( 3 , ( a - b ) z ) a 3 ( a - b ) 3 - Γ ( 3 , - ( a + b ) z ) a 3 ( a + b ) 3 + 3 Γ ( 2 , ( a - b ) z ) a 2 ( a - b ) 2 - 3 Γ ( 2 , - ( a + b ) z ) a 2 ( a + b ) 2 + 6 ( b - a ) z a a - b - 6 ( a + b ) z a a + b - 6 Ei ( ( b - a ) z ) + 6 Ei ( ( a + b ) z ) - Ei ( b z ) Γ ( 4 , - a z ) + Ei ( b z ) Γ ( 4 , a z ) ) + ( Ei ( b z ) z 4 + Γ ( 4 , - b z ) b 4 ) Shi ( a z ) ) z z 3 ExpIntegralEi b z SinhIntegral a z 1 4 -1 1 2 b 3 -1 Gamma 3 a -1 b z b 2 b -1 a 3 -1 -1 Gamma 3 -1 a b z b 2 a b 3 -1 3 Gamma 2 a -1 b z b a -1 b 2 -1 -1 3 Gamma 2 -1 a b z b a b 2 -1 6 b -1 a z b -1 a -1 -1 6 a b z a b -1 3 ExpIntegralEi b -1 a z -1 ExpIntegralEi a b z b 4 -1 -1 1 2 a 4 -1 Gamma 3 a -1 b z a 3 a -1 b 3 -1 -1 Gamma 3 -1 a b z a 3 a b 3 -1 3 Gamma 2 a -1 b z a 2 a -1 b 2 -1 -1 3 Gamma 2 -1 a b z a 2 a b 2 -1 6 b -1 a z a a -1 b -1 -1 6 a b z a a b -1 -1 6 ExpIntegralEi b -1 a z 6 ExpIntegralEi a b z -1 ExpIntegralEi b z Gamma 4 -1 a z ExpIntegralEi b z Gamma 4 a z ExpIntegralEi b z z 4 Gamma 4 -1 b z b 4 -1 SinhIntegral a z [/itex]

 Rule Form

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

 2001-10-29