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 Cos

 http://functions.wolfram.com/01.07.21.2602.01

 Input Form

 Integrate[E^(b z^2 + e) Sin[a z^2 + q] Cos[c z^2 + g]^v, z] == 2^(-2 - v) I E^(e + I q) Sqrt[Pi] Binomial[v, v/2] (Erfi[Sqrt[(-I) a + b] z]/(E^(2 I q) Sqrt[(-I) a + b]) - Erfi[Sqrt[I a + b] z]/Sqrt[I a + b]) (1 - Mod[v, 2]) + 2^(-2 - v) I Sqrt[Pi] Sum[Binomial[v, s] ((E^(e - I q - I g (-2 s + v)) Erfi[Sqrt[(-I) a + b - I c (-2 s + v)] z])/Sqrt[(-I) a + b - I c (-2 s + v)] - (E^(e + I q - I g (-2 s + v)) Erfi[Sqrt[I a + b - I c (-2 s + v)] z])/ Sqrt[I a + b - I c (-2 s + v)] + (E^(e - I q + I g (-2 s + v)) Erfi[Sqrt[(-I) a + b + I c (-2 s + v)] z])/ Sqrt[(-I) a + b + I c (-2 s + v)] - (E^(e + I q + I g (-2 s + v)) Erfi[Sqrt[I a + b + I c (-2 s + v)] z])/ Sqrt[I a + b + I c (-2 s + v)]), {s, 0, Floor[(1/2) (-1 + v)]}] /; Element[v, Integers] && v > 0

 Standard Form

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 MathML Form

 b z 2 + e sin ( a z 2 + q ) cos v ( c z 2 + g ) z 2 - v - 2 ( - 2 q erfi ( b - a z ) b - a - erfi ( b + a z ) b + a ) π ( v v 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox[FractionBox["v", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 1 - v mod 2 \$CellContext`v 2 ) e + q + 2 - v - 2 π s = 0 v - 1 2 ( v s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( e - q + g ( v - 2 s ) erfi ( b - a + c ( v - 2 s ) z ) b - a + c ( v - 2 s ) + e - q - g ( v - 2 s ) erfi ( b - a - c ( v - 2 s ) z ) b - a - c ( v - 2 s ) - e + q + g ( v - 2 s ) erfi ( b + a + c ( v - 2 s ) z ) b + a + c ( v - 2 s ) - e + q - g ( v - 2 s ) erfi ( b + a - c ( v - 2 s ) z ) b + a - c ( v - 2 s ) ) /; v + Condition z b z 2 e a z 2 q c z 2 g v 2 -1 v -2 -2 q Erfi b -1 a 1 2 z b -1 a 1 2 -1 -1 Erfi b a 1 2 z b a 1 2 -1 1 2 Binomial v v 2 -1 1 -1 \$CellContext`v 2 e q 2 -1 v -2 1 2 s 0 v -1 2 -1 Binomial v s e -1 q g v -1 2 s Erfi b -1 a c v -1 2 s 1 2 z b -1 a c v -1 2 s 1 2 -1 e -1 q -1 g v -1 2 s Erfi b -1 a -1 c v -1 2 s 1 2 z b -1 a -1 c v -1 2 s 1 2 -1 -1 e q g v -1 2 s Erfi b a c v -1 2 s 1 2 z b a c v -1 2 s 1 2 -1 -1 e q -1 g v -1 2 s Erfi b a -1 c v -1 2 s 1 2 z b a -1 c v -1 2 s 1 2 -1 v SuperPlus [/itex]

 Rule Form

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

 2002-12-18