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 SinhIntegral

 http://functions.wolfram.com/06.39.21.0071.01

 Input Form

 Integrate[z^3 SinIntegral[b z] SinhIntegral[a z], z] == (1/8) ((1/b^4) (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^3)) (I (-((6 E^((a - I b) z))/(I a + b)) + (6 I)/(E^((a + I b) z) (a + I b)) + (6 I E^((a + I b) z))/(a + I b) - (6 E^((-a) z + I b z))/(I a + b) - (3 b Gamma[2, (a - I b) z])/ (I a + b)^2 + (3 b Gamma[2, (-(a + I b)) z])/((-I) a + b)^2 + (3 b Gamma[2, (a + I b) z])/((-I) a + b)^2 - (3 b Gamma[2, (-a) z + I b z])/(I a + b)^2 - (b^2 Gamma[3, (a - I b) z])/(I a + b)^3 + (b^2 Gamma[3, (-(a + I b)) z])/((-I) a + b)^3 + (b^2 Gamma[3, (a + I b) z])/((-I) a + b)^3 - (b^2 Gamma[3, (-a) z + I b z])/(I a + b)^3)) + (1/b^4) (I (-Gamma[4, (-I) b z] + Gamma[4, I b z]) SinhIntegral[a z]) + 2 z^4 SinhIntegral[a z] SinIntegral[b z] + (1/(2 a^4)) (I (-((1/(a + I b)^3) ((a (-6 b^2 + a^4 z^2 + a^3 z (5 + 2 I b z) - 3 a b (-5 I + b z) + a^2 (11 + 8 I b z - b^2 z^2)))/ E^((a + I b) z))) + (1/(a - I b)^3) (a E^((a - I b) z) (-6 b^2 + a^4 z^2 + a^3 z (-5 - 2 I b z) + 3 a b (-5 I + b z) + a^2 (11 + 8 I b z - b^2 z^2))) + (1/(a - I b)^3) (a E^((-a) z + I b z) (-6 b^2 + a^4 z^2 + a^3 z (5 - 2 I b z) - 3 a b (5 I + b z) - a^2 (-11 + 8 I b z + b^2 z^2))) - (1/(a + I b)^3) (a E^((a + I b) z) (-6 b^2 + a^4 z^2 + a^3 z (-5 + 2 I b z) + 3 a b (5 I + b z) - a^2 (-11 + 8 I b z + b^2 z^2))) - 6 ExpIntegralEi[(a - I b) z] + 6 ExpIntegralEi[(-(a + I b)) z] + 6 ExpIntegralEi[(a + I b) z] - 6 ExpIntegralEi[(-a) z + I b z] + 2 I (-Gamma[4, (-a) z] + Gamma[4, a z]) SinIntegral[b z])))

 Standard Form

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 MathML Form

 z 3 Si ( b z ) Shi ( a z ) z 1 8 ( 2 Shi ( a z ) Si ( b z ) z 4 - 2 b 3 ( Γ ( 3 , - ( a + b ) z ) b 2 ( b - a ) 3 + Γ ( 3 , ( a + b ) z ) b 2 ( b - a ) 3 - Γ ( 3 , ( a - b ) z ) b 2 ( b + a ) 3 - Γ ( 3 , b z - a z ) b 2 ( b + a ) 3 + 3 Γ ( 2 , - ( a + b ) z ) b ( b - a ) 2 + 3 Γ ( 2 , ( a + b ) z ) b ( b - a ) 2 - 3 Γ ( 2 , ( a - b ) z ) b ( b + a ) 2 - 3 Γ ( 2 , b z - a z ) b ( b + a ) 2 + 6 - ( a + b ) z a + b + 6 ( a + b ) z a + b - 6 ( a - b ) z b + a - 6 b z - a z b + a ) + 1 b 4 ( 3 ( Ei ( - ( a + b ) z ) + Ei ( ( a + b ) z ) - Ei ( ( a - b ) z ) - Ei ( b z - a z ) ) ) + ( Γ ( 4 , b z ) - Γ ( 4 , - b z ) ) Shi ( a z ) b 4 + 1 2 a 4 ( ( - 1 ( a + b ) 3 ( a ( a + b ) z ( z 2 a 4 + z ( 2 b z - 5 ) a 3 - ( b 2 z 2 + 8 b z - 11 ) a 2 + 3 b ( 5 + b z ) a - 6 b 2 ) ) + 1 ( a - b ) 3 ( a b z - a z ( z 2 a 4 + z ( 5 - 2 b z ) a 3 - ( b 2 z 2 + 8 b z - 11 ) a 2 - 3 b ( 5 + b z ) a - 6 b 2 ) ) + 1 ( a - b ) 3 ( a ( a - b ) z ( z 2 a 4 + z ( - 2 b z - 5 ) a 3 + ( - b 2 z 2 + 8 b z + 11 ) a 2 + 3 b ( - 5 + b z ) a - 6 b 2 ) ) - 1 ( a + b ) 3 ( a - ( a + b ) z ( z 2 a 4 + z ( 2 b z + 5 ) a 3 + ( - b 2 z 2 + 8 b z + 11 ) a 2 - 3 b ( - 5 + b z ) a - 6 b 2 ) ) + 6 Ei ( - ( a + b ) z ) + 6 Ei ( ( a + b ) z ) - 6 Ei ( ( a - b ) z ) - 6 Ei ( b z - a z ) + 2 ( Γ ( 4 , a z ) - Γ ( 4 , - a z ) ) Si ( b z ) ) ) ) z z 3 SinIntegral b z SinhIntegral a z 1 8 2 SinhIntegral a z SinIntegral b z z 4 -1 2 b 3 -1 Gamma 3 -1 a b z b 2 b -1 a 3 -1 Gamma 3 a b z b 2 b -1 a 3 -1 -1 Gamma 3 a -1 b z b 2 b a 3 -1 -1 Gamma 3 b z -1 a z b 2 b a 3 -1 3 Gamma 2 -1 a b z b b -1 a 2 -1 3 Gamma 2 a b z b b -1 a 2 -1 -1 3 Gamma 2 a -1 b z b b a 2 -1 -1 3 Gamma 2 b z -1 a z b b a 2 -1 6 -1 a b z a b -1 6 a b z a b -1 -1 6 a -1 b z b a -1 -1 6 b z -1 a z b a -1 1 b 4 -1 3 ExpIntegralEi -1 a b z ExpIntegralEi a b z -1 ExpIntegralEi a -1 b z -1 ExpIntegralEi b z -1 a z Gamma 4 b z -1 Gamma 4 -1 b z SinhIntegral a z b 4 -1 1 2 a 4 -1 -1 1 a b 3 -1 a a b z z 2 a 4 z 2 b z -5 a 3 -1 b 2 z 2 8 b z -11 a 2 3 b 5 b z a -1 6 b 2 1 a -1 b 3 -1 a b z -1 a z z 2 a 4 z 5 -1 2 b z a 3 -1 b 2 z 2 8 b z -11 a 2 -1 3 b 5 b z a -1 6 b 2 1 a -1 b 3 -1 a a -1 b z z 2 a 4 z -2 b z -5 a 3 -1 b 2 z 2 8 b z 11 a 2 3 b -5 b z a -1 6 b 2 -1 1 a b 3 -1 a -1 a b z z 2 a 4 z 2 b z 5 a 3 -1 b 2 z 2 8 b z 11 a 2 -1 3 b -5 b z a -1 6 b 2 6 ExpIntegralEi -1 a b z 6 ExpIntegralEi a b z -1 6 ExpIntegralEi a -1 b z -1 6 ExpIntegralEi b z -1 a z 2 Gamma 4 a z -1 Gamma 4 -1 a z SinIntegral b z [/itex]

 Rule Form

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

 2001-10-29