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 CoshIntegral

 http://functions.wolfram.com/06.40.21.0081.01

 Input Form

 Integrate[z^2 SinhIntegral[b z] CoshIntegral[a z], z] == (1/12) ((1/b^3) (2 (ExpIntegralEi[(a - b) z] + ExpIntegralEi[(-a + b) z] + ExpIntegralEi[(-(a + b)) z] + ExpIntegralEi[(a + b) z])) - (1/b^3) (2 CoshIntegral[a z] (Gamma[3, (-b) z] + Gamma[3, b z])) - (-8 b Cosh[a z] Cosh[b z] + (a - b) b (a + b) z^2 (ExpIntegralE[-1, (a - b) z] + ExpIntegralE[-1, (-a + b) z] + ExpIntegralE[-1, (-(a + b)) z] + ExpIntegralE[-1, (a + b) z]) + 8 a Sinh[a z] Sinh[b z])/((a - b) b^2 (a + b)) + 4 z^3 CoshIntegral[a z] SinhIntegral[b z] - (1/a^3) (2 (ExpIntegralEi[(a - b) z] + ExpIntegralEi[(-a + b) z] - ExpIntegralEi[(-(a + b)) z] - ExpIntegralEi[(a + b) z] + (1/(a^2 - b^2)^2) (2 a (Cosh[b z] (2 b (-2 a^2 + b^2) Cosh[a z] + a (a - b) b (a + b) z Sinh[a z]) - a (a (a - b) (a + b) z Cosh[a z] + (-3 a^2 + b^2) Sinh[a z]) Sinh[b z])) + Gamma[3, (-a) z] SinhIntegral[b z] - Gamma[3, a z] SinhIntegral[b z])))

 Standard Form

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 MathML Form

 z 2 Shi ( b z ) Chi ( a z ) z 1 12 ( 4 Chi ( a z ) Shi ( b z ) z 3 + 1 b 3 ( 2 ( Ei ( ( a - b ) z ) + Ei ( ( b - a ) z ) + Ei ( - ( a + b ) z ) + Ei ( ( a + b ) z ) ) ) - 2 a 3 ( Ei ( ( a - b ) z ) + Ei ( ( b - a ) z ) - Ei ( - ( a + b ) z ) - Ei ( ( a + b ) z ) + 1 ( a 2 - b 2 ) 2 ( 2 a ( cosh ( b z ) ( 2 b ( b 2 - 2 a 2 ) cosh ( a z ) + a ( a - b ) b ( a + b ) z sinh ( a z ) ) - a ( a ( a - b ) ( a + b ) z cosh ( a z ) + ( b 2 - 3 a 2 ) sinh ( a z ) ) sinh ( b z ) ) ) + Γ ( 3 , - a z ) Shi ( b z ) - Γ ( 3 , a z ) Shi ( b z ) ) - 2 Chi ( a z ) ( Γ ( 3 , - b z ) + Γ ( 3 , b z ) ) b 3 - 1 ( a - b ) b 2 ( a + b ) ( ( a - b ) b ( a + b ) ( E TagBox["E", ExpIntegralE] - 1 ( ( a - b ) z ) + E TagBox["E", ExpIntegralE] - 1 ( ( b - a ) z ) + E TagBox["E", ExpIntegralE] - 1 ( - ( a + b ) z ) + E TagBox["E", ExpIntegralE] - 1 ( ( a + b ) z ) ) z 2 - 8 b cosh ( a z ) cosh ( b z ) + 8 a sinh ( a z ) sinh ( b z ) ) ) z z 2 SinhIntegral b z CoshIntegral a z 1 12 4 CoshIntegral a z SinhIntegral b z z 3 1 b 3 -1 2 ExpIntegralEi a -1 b z ExpIntegralEi b -1 a z ExpIntegralEi -1 a b z ExpIntegralEi a b z -1 2 a 3 -1 ExpIntegralEi a -1 b z ExpIntegralEi b -1 a z -1 ExpIntegralEi -1 a b z -1 ExpIntegralEi a b z 1 a 2 -1 b 2 2 -1 2 a b z 2 b b 2 -1 2 a 2 a z a a -1 b b a b z a z -1 a a a -1 b a b z a z b 2 -1 3 a 2 a z b z Gamma 3 -1 a z SinhIntegral b z -1 Gamma 3 a z SinhIntegral b z -1 2 CoshIntegral a z Gamma 3 -1 b z Gamma 3 b z b 3 -1 -1 1 a -1 b b 2 a b -1 a -1 b b a b ExpIntegralE -1 a -1 b z ExpIntegralE -1 b -1 a z ExpIntegralE -1 -1 a b z ExpIntegralE -1 a b z z 2 -1 8 b a z b z 8 a a z b z [/itex]

 Rule Form

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

 2001-10-29