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CoshIntegral






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > CoshIntegral[z] > Integration > Indefinite integration > Involving direct function and Gamma-, Beta-, Erf-type functions > Involving exponential integral-type functions and a power function > Involving Ci and power





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







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Rule Form





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





2001-10-29





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