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variants of this functions
Erf






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Erf[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving hyperbolic functions and a power function > Involving sinh and power





http://functions.wolfram.com/06.25.21.0079.01









  


  










Input Form





Integrate[z^3 Sinh[b z] Erf[a z], z] == (1/(16 a^6 b^4 Sqrt[Pi])) ((48 a^5 b - 4 a^3 b^3 + 2 a b^5 + 48 a^5 b E^(2 b z) - 4 a^3 b^3 E^(2 b z) + 2 a b^5 E^(2 b z) + 24 a^5 b^2 z - 4 a^3 b^4 z - 24 a^5 b^2 E^(2 b z) z + 4 a^3 b^4 E^(2 b z) z + 8 a^5 b^3 z^2 + 8 a^5 b^3 E^(2 b z) z^2 + 8 a^6 E^(a^2 z^2) Sqrt[Pi] (6 + 6 b z + 3 b^2 z^2 + b^3 z^3 + E^(2 b z) (-6 + 6 b z - 3 b^2 z^2 + b^3 z^3)) Erf[a z] - (48 a^6 - 12 a^4 b^2 - b^6) E^((b + 2 a^2 z)^2/(4 a^2)) Sqrt[Pi] Erf[b/(2 a) - a z] - 48 a^6 E^((b + 2 a^2 z)^2/(4 a^2)) Sqrt[Pi] Erf[b/(2 a) + a z] + 12 a^4 b^2 E^((b + 2 a^2 z)^2/(4 a^2)) Sqrt[Pi] Erf[b/(2 a) + a z] + b^6 E^((b + 2 a^2 z)^2/(4 a^2)) Sqrt[Pi] Erf[b/(2 a) + a z])/ E^(z (b + a^2 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