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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 Si and power





http://functions.wolfram.com/06.40.21.0072.01









  


  










Input Form





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










Standard Form





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MathML Form







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





2001-10-29