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 Cos

 http://functions.wolfram.com/01.07.21.2604.01

 Input Form

 Integrate[E^(b z^2 + d z + e) Sin[a z^2 + p z + q] Cos[c z^2 + f z + g]^v, z] == (1/(a^2 + b^2)) (2^(-2 - v) Sqrt[Pi] Binomial[v, v/2] ((Sqrt[(-I) a + b] (I a + b) Erfi[(d - I p - 2 I a z + 2 b z)/ (2 Sqrt[(-I) a + b])])/ E^(((d - I p)^2 - 4 ((-I) a + b) (e + (I Pi)/2 - I q))/ (4 ((-I) a + b))) + (((-I) a + b) Sqrt[I a + b] Erfi[(d + I p + 2 (I a + b) z)/(2 Sqrt[I a + b])])/ E^(((d + I p)^2 - 4 (I a + b) (e - (I Pi)/2 + I q))/(4 (I a + b)))) (1 - Mod[v, 2])) + 2^(-2 - v) Sqrt[Pi] Sum[Binomial[v, s] (((Sqrt[I a + b - I c (-2 s + v)] ((-I) a + b + I c (-2 s + v)) Erfi[(d + I p - I f (-2 s + v) + 2 b z - 2 ((-I) a + I c (-2 s + v)) z)/(2 Sqrt[I a + b - I c (-2 s + v)])])/ E^(((d + I p - I f (-2 s + v))^2 - 4 (I a + b - I c (-2 s + v)) (e - (I Pi)/2 + I q - I g (-2 s + v)))/ (4 (I a + b - I c (-2 s + v)))) + ((I a + b - I c (-2 s + v)) Sqrt[(-I) a + b + I c (-2 s + v)] Erfi[(d - I p + I f (-2 s + v) + 2 ((-I) a + b + I c (-2 s + v)) z)/(2 Sqrt[(-I) a + b + I c (-2 s + v)])])/E^(((d - I p + I f (-2 s + v))^2 - 4 ((-I) a + b + I c (-2 s + v)) (e + (I Pi)/2 - I q + I g (-2 s + v)))/(4 ((-I) a + b + I c (-2 s + v)))))/ ((I a + b - I c (-2 s + v)) ((-I) a + b + I c (-2 s + v))) + ((Sqrt[(-I) a + b - I c (-2 s + v)] (I a + b + I c (-2 s + v)) Erfi[(d - I p - I f (-2 s + v) + 2 b z - 2 (I a + I c (-2 s + v)) z)/(2 Sqrt[(-I) a + b - I c (-2 s + v)])])/ E^(((d - I p - I f (-2 s + v))^2 - 4 ((-I) a + b - I c (-2 s + v)) (e + (I Pi)/2 - I q - I g (-2 s + v)))/ (4 ((-I) a + b - I c (-2 s + v)))) + (((-I) a + b - I c (-2 s + v)) Sqrt[I a + b + I c (-2 s + v)] Erfi[(d + I p + I f (-2 s + v) + 2 (I a + b + I c (-2 s + v)) z)/ (2 Sqrt[I a + b + I c (-2 s + v)])])/ E^(((d + I p + I f (-2 s + v))^2 - 4 (I a + b + I c (-2 s + v)) (e - (I Pi)/2 + I q + I g (-2 s + v)))/ (4 (I a + b + I c (-2 s + v)))))/(((-I) a + b - I c (-2 s + v)) (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 + d z + e sin ( a z 2 + p z + q ) cos v ( c z 2 + f z + g ) z 1 a 2 + b 2 ( 2 - v - 2 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]]]]] ( b - a ( b + a ) - ( d - p ) 2 - 4 ( b - a ) ( e - q + π 2 ) 4 ( b - a ) erfi ( d - p - 2 a z + 2 b z 2 b - a ) + ( b - a ) b + a - ( d + p ) 2 - 4 ( b + a ) ( e + q - π 2 ) 4 ( b + a ) erfi ( d + p + 2 ( b + a ) z 2 b + a ) ) ( 1 - v mod 2 \$CellContext`v 2 ) ) + 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]]]]] ( ( - ( d - p + f ( v - 2 s ) ) 2 - 4 ( b - a + c ( v - 2 s ) ) ( e - q + g ( v - 2 s ) + π 2 ) 4 ( b - a + c ( v - 2 s ) ) b - a + c ( v - 2 s ) ( b + a - c ( v - 2 s ) ) erfi ( d - p + f ( v - 2 s ) + 2 ( b - a + c ( v - 2 s ) ) z 2 b - a + c ( v - 2 s ) ) + - ( d + p - f ( v - 2 s ) ) 2 - 4 ( b + a - c ( v - 2 s ) ) ( e + q - g ( v - 2 s ) - π 2 ) 4 ( b + a - c ( v - 2 s ) ) ( b - a + c ( v - 2 s ) ) b + a - c ( v - 2 s ) erfi ( d + p - f ( v - 2 s ) + 2 b z - 2 ( - a + c ( v - 2 s ) ) z 2 b + a - c ( v - 2 s ) ) ) / ( ( b + a - c ( v - 2 s ) ) ( b - a + c ( v - 2 s ) ) ) + ( - ( d + p + f ( v - 2 s ) ) 2 - 4 ( b + a + c ( v - 2 s ) ) ( e + q + g ( v - 2 s ) - π 2 ) 4 ( b + a + c ( v - 2 s ) ) b + a + c ( v - 2 s ) ( b - a - c ( v - 2 s ) ) erfi ( d + p + f ( v - 2 s ) + 2 ( b + a + c ( v - 2 s ) ) z 2 b + a + c ( v - 2 s ) ) + - ( d - p - f ( v - 2 s ) ) 2 - 4 ( b - a - c ( v - 2 s ) ) ( e - q - g ( v - 2 s ) + π 2 ) 4 ( b - a - c ( v - 2 s ) ) ( b + a + c ( v - 2 s ) ) b - a - c ( v - 2 s ) erfi ( d - p - f ( v - 2 s ) + 2 b z - 2 ( a + c ( v - 2 s ) ) z 2 b - a - c ( v - 2 s ) ) ) / ( ( b - a - c ( v - 2 s ) ) ( b + a + c ( v - 2 s ) ) ) ) /; v + Condition z b z 2 d z e a z 2 p z q c z 2 f z g v 1 a 2 b 2 -1 2 -1 v -2 1 2 Binomial v v 2 -1 b -1 a 1 2 b a -1 d -1 p 2 -1 4 b -1 a e -1 q 2 -1 4 b -1 a -1 Erfi d -1 p -1 2 a z 2 b z 2 b -1 a 1 2 -1 b -1 a b a 1 2 -1 d p 2 -1 4 b a e q -1 2 -1 4 b a -1 Erfi d p 2 b a z 2 b a 1 2 -1 1 -1 \$CellContext`v 2 2 -1 v -2 1 2 s 0 v -1 2 -1 Binomial v s -1 d -1 p f v -1 2 s 2 -1 4 b -1 a c v -1 2 s e -1 q g v -1 2 s 2 -1 4 b -1 a c v -1 2 s -1 b -1 a c v -1 2 s 1 2 b a -1 c v -1 2 s Erfi d -1 p f v -1 2 s 2 b -1 a c v -1 2 s z 2 b -1 a c v -1 2 s 1 2 -1 -1 d p -1 f v -1 2 s 2 -1 4 b a -1 c v -1 2 s e q -1 g v -1 2 s -1 2 -1 4 b a -1 c v -1 2 s -1 b -1 a c v -1 2 s b a -1 c v -1 2 s 1 2 Erfi d p -1 f v -1 2 s 2 b z -1 2 -1 a c v -1 2 s z 2 b a -1 c v -1 2 s 1 2 -1 b a -1 c v -1 2 s b -1 a c v -1 2 s -1 -1 d p f v -1 2 s 2 -1 4 b a c v -1 2 s e q g v -1 2 s -1 2 -1 4 b a c v -1 2 s -1 b a c v -1 2 s 1 2 b -1 a -1 c v -1 2 s Erfi d p f v -1 2 s 2 b a c v -1 2 s z 2 b a c v -1 2 s 1 2 -1 -1 d -1 p -1 f v -1 2 s 2 -1 4 b -1 a -1 c v -1 2 s e -1 q -1 g v -1 2 s 2 -1 4 b -1 a -1 c v -1 2 s -1 b a c v -1 2 s b -1 a -1 c v -1 2 s 1 2 Erfi d -1 p -1 f v -1 2 s 2 b z -1 2 a c v -1 2 s z 2 b -1 a -1 c v -1 2 s 1 2 -1 b -1 a -1 c v -1 2 s b a c v -1 2 s -1 v SuperPlus [/itex]

 Rule Form

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

 2002-12-18