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 Erfc

 http://functions.wolfram.com/06.27.21.0088.01

 Input Form

 Integrate[z^3 Cosh[b z] Erfc[a z], z] == (1/(16 a^6 b^4 Sqrt[Pi])) (((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 - 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] - 2 a (b (b^4 (-1 + E^(2 b z)) + 2 a^2 b^2 (1 + b z + E^(2 b z) (-1 + b z)) + 4 a^4 (-6 - 3 b z - b^2 z^2 + E^(2 b z) (6 - 3 b z + b^2 z^2))) + 4 a^5 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)) Erfc[a z]))/E^(z (b + a^2 z)))

 Standard Form

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 MathML Form

 z 3 cosh ( b z ) erfc ( a z ) z 1 16 a 6 b 4 π ( - z ( z a 2 + b ) ( - ( 48 a 6 - 12 b 2 a 4 - b 6 ) ( 2 z a 2 + b ) 2 4 a 2 π erf ( b 2 a + a z ) + ( 48 a 6 - 12 b 2 a 4 - b 6 ) ( 2 z a 2 + b ) 2 4 a 2 π erf ( b 2 a - a z ) - 2 a ( 4 a 2 z 2 π ( b 3 z 3 + 3 b 2 z 2 + 6 b z + 2 b z ( - b 3 z 3 + 3 b 2 z 2 - 6 b z + 6 ) + 6 ) erfc ( a z ) a 5 + b ( 4 ( - b 2 z 2 - 3 b z + 2 b z ( b 2 z 2 - 3 b z + 6 ) - 6 ) a 4 + 2 b 2 ( b z + 2 b z ( b z - 1 ) + 1 ) a 2 + b 4 ( - 1 + 2 b z ) ) ) ) ) z z 3 b z Erfc a z 1 16 a 6 b 4 1 2 -1 -1 z z a 2 b -1 48 a 6 -1 12 b 2 a 4 -1 b 6 2 z a 2 b 2 4 a 2 -1 1 2 Erf b 2 a -1 a z 48 a 6 -1 12 b 2 a 4 -1 b 6 2 z a 2 b 2 4 a 2 -1 1 2 Erf b 2 a -1 -1 a z -1 2 a 4 a 2 z 2 1 2 b 3 z 3 3 b 2 z 2 6 b z 2 b z -1 b 3 z 3 3 b 2 z 2 -1 6 b z 6 6 Erfc a z a 5 b 4 -1 b 2 z 2 -1 3 b z 2 b z b 2 z 2 -1 3 b z 6 -6 a 4 2 b 2 b z 2 b z b z -1 1 a 2 b 4 -1 2 b z [/itex]

 Rule Form

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

 2001-10-29