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 Cosh

 http://functions.wolfram.com/01.20.21.0498.01

 Input Form

 Integrate[E^(b z^2 + d z + e) Cosh[c z^2 + f z + g], z] == (1/(4 (b - c) (b + c))) ((Sqrt[Pi] (Sqrt[b - c] (b + c) E^((b (d^2 + 4 d f + f^2))/ (4 (b - c) (b + c))) Erfi[(d - f + 2 b z - 2 c z)/(2 Sqrt[b - c])] (Cosh[g] - Sinh[g]) + (b - c) Sqrt[b + c] E^(((b + 2 c) (d^2 + f^2))/(4 (b - c) (b + c))) Erfi[(d + f + 2 (b + c) z)/(2 Sqrt[b + c])] (Cosh[g] + Sinh[g])))/ E^((-4 b^2 e + c (d^2 + 4 c e - 2 d f + f^2) + 2 b (d^2 + d f + f^2))/ (4 (b^2 - c^2))))

 Standard Form

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 MathML Form

 b z 2 + d z + e cosh ( c z 2 + f z + g ) z 1 4 ( b - c ) ( b + c ) ( - - 4 e b 2 + 2 ( d 2 + f d + f 2 ) b + c ( d 2 - 2 f d + f 2 + 4 c e ) 4 ( b 2 - c 2 ) π ( b - c ( b + c ) b ( d 2 + 4 f d + f 2 ) 4 ( b - c ) ( b + c ) erfi ( d - f + 2 b z - 2 c z 2 b - c ) ( cosh ( g ) - sinh ( g ) ) + ( b - c ) b + c ( b + 2 c ) ( d 2 + f 2 ) 4 ( b - c ) ( b + c ) erfi ( d + f + 2 ( b + c ) z 2 b + c ) ( cosh ( g ) + sinh ( g ) ) ) ) z b z 2 d z e c z 2 f z g 1 4 b -1 c b c -1 -1 -4 e b 2 2 d 2 f d f 2 b c d 2 -1 2 f d f 2 4 c e 4 b 2 -1 c 2 -1 1 2 b -1 c 1 2 b c b d 2 4 f d f 2 4 b -1 c b c -1 Erfi d -1 f 2 b z -1 2 c z 2 b -1 c 1 2 -1 g -1 g b -1 c b c 1 2 b 2 c d 2 f 2 4 b -1 c b c -1 Erfi d f 2 b c z 2 b c 1 2 -1 g g [/itex]

 Rule Form

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

 2002-12-18