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 Erfc

 http://functions.wolfram.com/06.27.21.0077.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2001-10-29