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 Erfc

 http://functions.wolfram.com/06.27.21.0108.01

 Input Form

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

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

 Rule Form

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

 2001-10-29