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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 power, exponential and hyperbolic functions > Involving power, exp and cosh





http://functions.wolfram.com/06.25.21.0111.01









  


  










Input Form





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










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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