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 Erf

 http://functions.wolfram.com/06.25.21.0066.01

 Input Form

 Integrate[z^2 E^(b z) Cos[c z] Erf[a z], z] == ((1/(8 a^4 Sqrt[Pi])) ((1/(b - I c)^3) (2 a (b - I c) E^((b - I c) z) ((b - I c)^2 + 2 a^2 (-2 + b z - I c z)) + 4 a^4 E^(z (b - I c + a^2 z)) Sqrt[Pi] (2 - 2 (b - I c) z + (b - I c)^2 z^2) Erf[a z] + (8 a^4 - 2 a^2 (b - I c)^2 + (b - I c)^4) 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)^3) (2 a (b + I c) E^((b + I c) z) ((b + I c)^2 + 2 a^2 (-2 + b z + I c z)) + 4 a^4 E^(z (b + I c + a^2 z)) Sqrt[Pi] (2 - 2 (b + I c) z + (b + I c)^2 z^2) Erf[a z] + (8 a^4 - 2 a^2 (b + I c)^2 + (b + I c)^4) 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 2 b z cos ( c z ) erf ( a z ) z 1 8 a 4 π - a 2 z 2 ( 1 ( b - c ) 3 ( 4 z ( z a 2 + b - c ) π ( ( b - c ) 2 z 2 - 2 ( b - c ) z + 2 ) erf ( a z ) a 4 + 2 ( b - c ) ( b - c ) z ( 2 ( b z - c z - 2 ) a 2 + ( b - c ) 2 ) a + ( 8 a 4 - 2 ( b - c ) 2 a 2 + ( b - c ) 4 ) exp ( ( b - c ) 2 4 a 2 + a 2 z 2 ) π erf ( b - c 2 a - a z ) ) + 1 ( b + c ) 3 ( 4 z ( z a 2 + b + c ) π ( ( b + c ) 2 z 2 - 2 ( b + c ) z + 2 ) erf ( a z ) a 4 + 2 ( b + c ) ( b + c ) z ( 2 ( b z + c z - 2 ) a 2 + ( b + c ) 2 ) a + ( 8 a 4 - 2 ( b + c ) 2 a 2 + ( b + c ) 4 ) exp ( ( b + c ) 2 4 a 2 + a 2 z 2 ) π erf ( b + c 2 a - a z ) ) ) z z 2 b z c z Erf a z 1 8 a 4 1 2 -1 -1 a 2 z 2 1 b -1 c 3 -1 4 z z a 2 b -1 c 1 2 b -1 c 2 z 2 -1 2 b -1 c z 2 Erf a z a 4 2 b -1 c b -1 c z 2 b z -1 c z -2 a 2 b -1 c 2 a 8 a 4 -1 2 b -1 c 2 a 2 b -1 c 4 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 b c 3 -1 4 z z a 2 b c 1 2 b c 2 z 2 -1 2 b c z 2 Erf a z a 4 2 b c b c z 2 b z c z -2 a 2 b c 2 a 8 a 4 -1 2 b c 2 a 2 b c 4 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