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 SinhIntegral

 http://functions.wolfram.com/06.39.21.0074.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2001-10-29