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 Erfc

 http://functions.wolfram.com/06.27.21.0087.01

 Input Form

 Integrate[z^2 Cosh[b z] Erfc[a z], z] == (1/(8 a^4 b^3 Sqrt[Pi])) ((8 a^3 b - 2 a b^3 + 8 a^3 b E^(2 b z) - 2 a b^3 E^(2 b z) + 4 a^3 b^2 z - 4 a^3 b^2 E^(2 b z) z - (8 a^4 - 2 a^2 b^2 + b^4) E^((b + 2 a^2 z)^2/(4 a^2)) Sqrt[Pi] Erf[b/(2 a) - a z] - (8 a^4 - 2 a^2 b^2 + b^4) E^((b + 2 a^2 z)^2/(4 a^2)) Sqrt[Pi] Erf[b/(2 a) + a z] - 8 a^4 E^(a^2 z^2) Sqrt[Pi] Erfc[a z] + 8 a^4 E^(z (2 b + a^2 z)) Sqrt[Pi] Erfc[a z] - 8 a^4 b E^(a^2 z^2) Sqrt[Pi] z Erfc[a z] - 8 a^4 b E^(z (2 b + a^2 z)) Sqrt[Pi] z Erfc[a z] + 8 a^4 b^2 E^(z (b + a^2 z)) Sqrt[Pi] z^2 Erfc[a z] Sinh[b z])/E^(z (b + a^2 z)))

 Standard Form

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 MathML Form

 z 2 cosh ( b z ) erfc ( a z ) z 1 8 a 4 b 3 π ( - z ( z a 2 + b ) ( - 8 b a 2 z 2 π z erfc ( a z ) a 4 - 8 b z ( z a 2 + 2 b ) π z erfc ( a z ) a 4 - 8 a 2 z 2 π erfc ( a z ) a 4 + 8 z ( z a 2 + 2 b ) π erfc ( a z ) a 4 + 8 b 2 z ( z a 2 + b ) π z 2 erfc ( a z ) sinh ( b z ) a 4 + 8 b 2 b z a 3 + 8 b a 3 - 4 b 2 2 b z z a 3 + 4 b 2 z a 3 - 2 b 3 2 b z a - 2 b 3 a - ( 8 a 4 - 2 b 2 a 2 + b 4 ) ( 2 z a 2 + b ) 2 4 a 2 π erf ( b 2 a + a z ) - ( 8 a 4 - 2 b 2 a 2 + b 4 ) ( 2 z a 2 + b ) 2 4 a 2 π erf ( b 2 a - a z ) ) ) z z 2 b z Erfc a z 1 8 a 4 b 3 1 2 -1 -1 z z a 2 b -8 b a 2 z 2 1 2 z Erfc a z a 4 -1 8 b z z a 2 2 b 1 2 z Erfc a z a 4 -1 8 a 2 z 2 1 2 Erfc a z a 4 8 z z a 2 2 b 1 2 Erfc a z a 4 8 b 2 z z a 2 b 1 2 z 2 Erfc a z b z a 4 8 b 2 b z a 3 8 b a 3 -1 4 b 2 2 b z z a 3 4 b 2 z a 3 -1 2 b 3 2 b z a -1 2 b 3 a -1 8 a 4 -1 2 b 2 a 2 b 4 2 z a 2 b 2 4 a 2 -1 1 2 Erf b 2 a -1 a z -1 8 a 4 -1 2 b 2 a 2 b 4 2 z a 2 b 2 4 a 2 -1 1 2 Erf b 2 a -1 -1 a z [/itex]

 Rule Form

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

 2001-10-29