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 CoshIntegral

 http://functions.wolfram.com/06.40.21.0076.01

 Input Form

 Integrate[z^2 CosIntegral[b z] CoshIntegral[a z], z] == (1/6) (2 z^3 CoshIntegral[a z] CosIntegral[b z] + (I/b^3) (-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/(a^2 + b^2)) (b (a^2 + b^2) z^2 (ExpIntegralE[-1, (a - I b) z] + ExpIntegralE[-1, (-(a + I b)) z] - ExpIntegralE[-1, (a + I b) z] - ExpIntegralE[-1, (-a) z + I b z]) - 8 I b Cosh[a z] Sin[b z] - 8 I a Cos[b z] Sinh[a z])) - (1/a^3) (((2 a)/(a^2 + b^2)^2) (a Cos[b z] ((-a) (a^2 + b^2) z Cosh[a z] + (3 a^2 + b^2) Sinh[a z]) + b Sin[b z] (2 (2 a^2 + b^2) Cosh[a z] - a (a^2 + b^2) z Sinh[a z])) - ExpIntegralEi[(a - I b) z] + ExpIntegralEi[(-(a + I b)) z] - ExpIntegralEi[(a + I b) z] + ExpIntegralEi[(-a) z + I b z] + CosIntegral[b z] (Gamma[3, (-a) z] - Gamma[3, a z])) - (1/b^3) (I CoshIntegral[a z] (Gamma[3, (-I) b z] - Gamma[3, I b z])))

 Standard Form

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 MathML Form

 z 2 Ci ( b z ) Chi ( a z ) z 1 6 ( 2 Chi ( a z ) Ci ( b z ) z 3 + 1 b 3 ( ( - Ei ( - ( a + b ) z ) + Ei ( ( a + b ) z ) - Ei ( ( a - b ) z ) + Ei ( b z - a z ) ) ) - 1 a 3 ( Ei ( - ( a + b ) z ) - Ei ( ( a + b ) z ) - Ei ( ( a - b ) z ) + Ei ( b z - a z ) + Ci ( b z ) ( Γ ( 3 , - a z ) - Γ ( 3 , a z ) ) + 2 a ( a 2 + b 2 ) 2 ( a cos ( b z ) ( ( 3 a 2 + b 2 ) sinh ( a z ) - a ( a 2 + b 2 ) z cosh ( a z ) ) + b sin ( b z ) ( 2 ( 2 a 2 + b 2 ) cosh ( a z ) - a ( a 2 + b 2 ) z sinh ( a z ) ) ) ) + 2 b 2 ( a 2 + b 2 ) ( b ( a 2 + b 2 ) ( E TagBox["E", ExpIntegralE] - 1 ( - ( a + b ) z ) - E TagBox["E", ExpIntegralE] - 1 ( ( a + b ) z ) + E TagBox["E", ExpIntegralE] - 1 ( ( a - b ) z ) - E TagBox["E", ExpIntegralE] - 1 ( b z - a z ) ) z 2 - 8 b cosh ( a z ) sin ( b z ) - 8 a cos ( b z ) sinh ( a z ) ) - Chi ( a z ) ( Γ ( 3 , - b z ) - Γ ( 3 , b z ) ) b 3 ) z z 2 CosIntegral b z CoshIntegral a z 1 6 2 CoshIntegral a z CosIntegral b z z 3 1 b 3 -1 -1 ExpIntegralEi -1 a b z ExpIntegralEi a b z -1 ExpIntegralEi a -1 b z ExpIntegralEi b z -1 a z -1 1 a 3 -1 ExpIntegralEi -1 a b z -1 ExpIntegralEi a b z -1 ExpIntegralEi a -1 b z ExpIntegralEi b z -1 a z CosIntegral b z Gamma 3 -1 a z -1 Gamma 3 a z 2 a a 2 b 2 2 -1 a b z 3 a 2 b 2 a z -1 a a 2 b 2 z a z b b z 2 2 a 2 b 2 a z -1 a a 2 b 2 z a z 2 b 2 a 2 b 2 -1 b a 2 b 2 ExpIntegralE -1 -1 a b z -1 ExpIntegralE -1 a b z ExpIntegralE -1 a -1 b z -1 ExpIntegralE -1 b z -1 a z z 2 -1 8 b a z b z -1 8 a b z a z -1 CoshIntegral a z Gamma 3 -1 b z -1 Gamma 3 b z b 3 -1 [/itex]

 Rule Form

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

 2001-10-29