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 Cos

 http://functions.wolfram.com/01.07.21.2586.01

 Input Form

 Integrate[E^(p z^2) Sin[b z^2] Cos[c z]^v, z] == 2^(-2 - v) Sqrt[Pi] ((1/(b^2 + p^2)) (Binomial[v, v/2] ((b - I p) Sqrt[(-I) b + p] Erfi[Sqrt[(-I) b + p] z] + (b + I p) Sqrt[I b + p] Erfi[Sqrt[I b + p] z]) (-1 + Mod[v, 2])) + I Sum[(1/(b^2 + p^2)) Binomial[v, s] (E^((c^2 (-2 s + v)^2)/(4 ((-I) b + p))) (b - I p) Sqrt[(-I) b + p] Erf[(c (-2 s + v) + 2 (b + I p) z)/(2 Sqrt[(-I) b + p])] + I E^((c^2 (-2 s + v)^2)/(4 (I b + p))) (b + I p) Sqrt[I b + p] Erfi[((-I) c (-2 s + v) + 2 I b z + 2 p z)/(2 Sqrt[I b + p])] + E^((c^2 (-2 s + v)^2)/(4 ((-I) b + p))) Sqrt[(-I) b + p] (I b + p) Erfi[(I c (-2 s + v) + 2 ((-I) b + p) z)/(2 Sqrt[(-I) b + p])] + I E^((c^2 (-2 s + v)^2)/(4 (I b + p))) (b + I p) Sqrt[I b + p] Erfi[(I c (-2 s + v) + 2 (I b + p) z)/(2 Sqrt[I b + p])]), {s, 0, Floor[(1/2) (-1 + v)]}]) /; Element[v, Integers] && v > 0

 Standard Form

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"+", "p"]]]]]], "]"]]]]]], ")"]]]]]]]]]], ")"]]]]]], "/;", RowBox[List[RowBox[List["v", "\[Element]", "Integers"]], "\[And]", RowBox[List["v", ">", "0"]]]]]]]]

 MathML Form

 p z 2 sin ( b z 2 ) cos v ( c z ) z 2 - v - 2 π ( 1 b 2 + p 2 ( ( v v 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity, Rule[Editable, True]]], List[TagBox[FractionBox["v", "2"], Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( - b + p ( b - p ) erfi ( - b + p z ) + b + p ( b + p ) erfi ( b + p z ) ) ( v mod 2 \$CellContext`v 2 - 1 ) ) + s = 0 v - 1 2 1 b 2 + p 2 ( ( v s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity, Rule[Editable, True]]], List[TagBox["s", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( c 2 ( v - 2 s ) 2 4 ( - b + p ) - b + p ( b - p ) erf ( c ( v - 2 s ) + 2 ( b + p ) z 2 - b + p ) + c 2 ( v - 2 s ) 2 4 ( - b + p ) - b + p ( b + p ) erfi ( c ( v - 2 s ) + 2 ( - b + p ) z 2 - b + p ) + c 2 ( v - 2 s ) 2 4 ( b + p ) b + p ( b + p ) erfi ( - c ( v - 2 s ) + 2 b z + 2 p z 2 b + p ) + c 2 ( v - 2 s ) 2 4 ( b + p ) b + p ( b + p ) erfi ( c ( v - 2 s ) + 2 ( b + p ) z 2 b + p ) ) ) ) /; v + Condition z p z 2 b z 2 c z v 2 -1 v -2 1 2 1 b 2 p 2 -1 Binomial v v 2 -1 -1 b p 1 2 b -1 p Erfi -1 b p 1 2 z b p 1 2 b p Erfi b p 1 2 z \$CellContext`v 2 -1 s 0 v -1 2 -1 1 b 2 p 2 -1 Binomial v s c 2 v -1 2 s 2 4 -1 b p -1 -1 b p 1 2 b -1 p Erf c v -1 2 s 2 b p z 2 -1 b p 1 2 -1 c 2 v -1 2 s 2 4 -1 b p -1 -1 b p 1 2 b p Erfi c v -1 2 s 2 -1 b p z 2 -1 b p 1 2 -1 c 2 v -1 2 s 2 4 b p -1 b p 1 2 b p Erfi -1 c v -1 2 s 2 b z 2 p z 2 b p 1 2 -1 c 2 v -1 2 s 2 4 b p -1 b p 1 2 b p Erfi c v -1 2 s 2 b p z 2 b p 1 2 -1 v SuperPlus [/itex]

 Rule Form

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

 2002-12-18