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 Erfc

 http://functions.wolfram.com/06.27.21.0058.01

 Input Form

 Integrate[z^3 E^(b z) Sin[c z] Erfc[a z], z] == (1/(b^2 + c^2)^4) (E^(b z) ((-c) (-6 b^5 z^2 + b^6 z^3 + c^4 z (-6 + c^2 z^2) - 6 b c^2 (-4 + c^2 z^2) - 12 b^3 (2 + c^2 z^2) + 3 b^2 c^2 z (4 + c^2 z^2) + 3 b^4 z (6 + c^2 z^2)) Cos[c z] + (-3 b^6 z^2 + b^7 z^3 + b c^4 z (-18 + c^2 z^2) + 3 b^3 c^2 z (-4 + c^2 z^2) + 3 c^4 (-2 + c^2 z^2) - 3 b^4 (2 + c^2 z^2) + 3 b^5 z (2 + c^2 z^2) + 3 b^2 c^2 (12 + c^2 z^2)) Sin[c z])) - ((I/(16 a^6 Sqrt[Pi])) ((1/(b - I c)^4) (2 a (b - I c) E^((b - I c) z) ((b - I c)^4 + 2 a^2 (b - I c)^2 (-1 + b z - I c z) + 4 a^4 (6 - 3 (b - I c) z + (b - I c)^2 z^2)) + 8 a^6 E^(z (b - I c + a^2 z)) Sqrt[Pi] (-6 + 6 (b - I c) z - 3 (b - I c)^2 z^2 + (b - I c)^3 z^3) Erf[a z] - (48 a^6 - 12 a^4 (b - I c)^2 - (b - I c)^6) E^((b - I c)^2/(4 a^2) + a^2 z^2) Sqrt[Pi] Erf[(b - I c)/(2 a) - a z]) - (1/(b + I c)^4) (2 a (b + I c) E^((b + I c) z) ((b + I c)^4 + 2 a^2 (b + I c)^2 (-1 + b z + I c z) + 4 a^4 (6 - 3 (b + I c) z + (b + I c)^2 z^2)) + 8 a^6 E^(z (b + I c + a^2 z)) Sqrt[Pi] (-6 + 6 (b + I c) z - 3 (b + I c)^2 z^2 + (b + I c)^3 z^3) Erf[a z] - (48 a^6 - 12 a^4 (b + I c)^2 - (b + I c)^6) E^((b + I c)^2/(4 a^2) + a^2 z^2) Sqrt[Pi] Erf[(b + I c)/(2 a) - a z])))/E^(a^2 z^2)

 Standard Form

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 MathML Form

 z 3 b z sin ( c z ) erfc ( a z ) z 1 ( b 2 + c 2 ) 4 ( b z ( ( z 3 b 7 - 3 z 2 b 6 + 3 z ( c 2 z 2 + 2 ) b 5 - 3 ( c 2 z 2 + 2 ) b 4 + 3 c 2 z ( c 2 z 2 - 4 ) b 3 + 3 c 2 ( c 2 z 2 + 12 ) b 2 + c 4 z ( c 2 z 2 - 18 ) b + 3 c 4 ( c 2 z 2 - 2 ) ) sin ( c z ) - c ( z 3 b 6 - 6 z 2 b 5 + 3 z ( c 2 z 2 + 6 ) b 4 - 12 ( c 2 z 2 + 2 ) b 3 + 3 c 2 z ( c 2 z 2 + 4 ) b 2 - 6 c 2 ( c 2 z 2 - 4 ) b + c 4 z ( c 2 z 2 - 6 ) ) cos ( c z ) ) ) - 16 a 6 π - a 2 z 2 ( 1 ( b - c ) 4 ( 8 z ( z a 2 + b - c ) π ( ( b - c ) 3 z 3 - 3 ( b - c ) 2 z 2 + 6 ( b - c ) z - 6 ) erf ( a z ) a 6 + 2 ( b - c ) ( b - c ) z ( 4 ( ( b - c ) 2 z 2 - 3 ( b - c ) z + 6 ) a 4 + 2 ( b - c ) 2 ( b z - c z - 1 ) a 2 + ( b - c ) 4 ) a - ( 48 a 6 - 12 ( b - c ) 2 a 4 - ( b - c ) 6 ) exp ( ( b - c ) 2 4 a 2 + a 2 z 2 ) π erf ( b - c 2 a - a z ) ) - 1 ( b + c ) 4 ( 8 z ( z a 2 + b + c ) π ( ( b + c ) 3 z 3 - 3 ( b + c ) 2 z 2 + 6 ( b + c ) z - 6 ) erf ( a z ) a 6 + 2 ( b + c ) ( b + c ) z ( 4 ( ( b + c ) 2 z 2 - 3 ( b + c ) z + 6 ) a 4 + 2 ( b + c ) 2 ( b z + c z - 1 ) a 2 + ( b + c ) 4 ) a - ( 48 a 6 - 12 ( b + c ) 2 a 4 - ( b + c ) 6 ) exp ( ( b + c ) 2 4 a 2 + a 2 z 2 ) π erf ( b + c 2 a - a z ) ) ) z z 3 b z c z Erfc a z 1 b 2 c 2 4 -1 b z z 3 b 7 -1 3 z 2 b 6 3 z c 2 z 2 2 b 5 -1 3 c 2 z 2 2 b 4 3 c 2 z c 2 z 2 -4 b 3 3 c 2 c 2 z 2 12 b 2 c 4 z c 2 z 2 -18 b 3 c 4 c 2 z 2 -2 c z -1 c z 3 b 6 -1 6 z 2 b 5 3 z c 2 z 2 6 b 4 -1 12 c 2 z 2 2 b 3 3 c 2 z c 2 z 2 4 b 2 -1 6 c 2 c 2 z 2 -4 b c 4 z c 2 z 2 -6 c z -1 16 a 6 1 2 -1 -1 a 2 z 2 1 b -1 c 4 -1 8 z z a 2 b -1 c 1 2 b -1 c 3 z 3 -1 3 b -1 c 2 z 2 6 b -1 c z -6 Erf a z a 6 2 b -1 c b -1 c z 4 b -1 c 2 z 2 -1 3 b -1 c z 6 a 4 2 b -1 c 2 b z -1 c z -1 a 2 b -1 c 4 a -1 48 a 6 -1 12 b -1 c 2 a 4 -1 b -1 c 6 b -1 c 2 4 a 2 -1 a 2 z 2 1 2 Erf b -1 c 2 a -1 -1 a z -1 1 b c 4 -1 8 z z a 2 b c 1 2 b c 3 z 3 -1 3 b c 2 z 2 6 b c z -6 Erf a z a 6 2 b c b c z 4 b c 2 z 2 -1 3 b c z 6 a 4 2 b c 2 b z c z -1 a 2 b c 4 a -1 48 a 6 -1 12 b c 2 a 4 -1 b c 6 b c 2 4 a 2 -1 a 2 z 2 1 2 Erf b 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