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 Cos

 http://functions.wolfram.com/01.07.21.2607.01

 Input Form

 Integrate[(E^(p z) Sin[e z] Cos[c z]^v)/(a + b E^(d z))^n, z] == -((I 2^(-1 - v) Binomial[v, v/2] (E^(((-I) e + p) z) (I e + p) Hypergeometric2F1[((-I) e + p)/d, n, (d - I e + p)/d, -((b E^(d z))/a)] + E^((I e + p) z) (I e - p) Hypergeometric2F1[(I e + p)/d, n, (d + I e + p)/d, -((b E^(d z))/a)]) (1 - Mod[v, 2]))/a^n/((I e - p) (I e + p))) + (I 2^(-1 - v) Sum[Binomial[v, s] ((E^((I e + p + 2 I c s - I c v) z) ((-I) e + p - 2 I c s + I c v) Hypergeometric2F1[(I e + p + 2 I c s - I c v)/d, n, (d + I e + p + 2 I c s - I c v)/d, -((b E^(d z))/a)] + E^(((-I) e + p - 2 I c s + I c v) z) ((-I) e - p - 2 I c s + I c v) Hypergeometric2F1[((-I) e + p - 2 I c s + I c v)/d, n, (d - I e + p - 2 I c s + I c v)/d, -((b E^(d z))/a)])/ (((-I) e - p - 2 I c s + I c v) ((-I) e + p - 2 I c s + I c v)) + (E^(((-I) e + p + 2 I c s - I c v) z) ((-I) e - p + 2 I c s - I c v) Hypergeometric2F1[((-I) e + p + 2 I c s - I c v)/d, n, (d - I e + p + 2 I c s - I c v)/d, -((b E^(d z))/a)] + E^((I e + p - 2 I c s + I c v) z) ((-I) e + p + 2 I c s - I c v) Hypergeometric2F1[(I e + p - 2 I c s + I c v)/d, n, (d + I e + p - 2 I c s + I c v)/d, -((b E^(d z))/a)])/ (((-I) e - p + 2 I c s - I c v) ((-I) e + p + 2 I c s - I c v))), {s, 0, Floor[(1/2) (-1 + v)]}])/a^n /; Element[n, Integers] && n > 0 && Element[v, Integers] && v > 0

 Standard Form

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 MathML Form

 p z sin ( e z ) cos v ( c z ) ( a + b d z ) n z 2 - v - 1 a - n 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 + p - 2 c s + c v ) z ( - e - p - 2 c s + c v ) 2 F 1 ( - e + p - 2 c s + c v d , n ; d - e + p - 2 c s + c v d ; - b d z a ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "e"]], "+", "p", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "c", " ", "s"]], "+", RowBox[List["\[ImaginaryI]", " ", "c", " ", "v"]]]], "d"], Hypergeometric2F1], ",", TagBox["n", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[FractionBox[RowBox[List["d", "-", RowBox[List["\[ImaginaryI]", " ", "e"]], "+", "p", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "c", " ", "s"]], "+", RowBox[List["\[ImaginaryI]", " ", "c", " ", "v"]]]], "d"], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[RowBox[List["-", FractionBox[RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["d", " ", "z"]]]]], "a"]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] + ( e + p + 2 c s - c v ) z ( - e + p - 2 c s + c v ) 2 F 1 ( e + p + 2 c s - c v d , n ; 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n + v + Condition z p z e z c z v a b d z n -1 2 -1 v -1 a -1 n s 0 v -1 2 -1 Binomial v s -1 e p -1 2 c s c v z -1 e -1 p -1 2 c s c v Hypergeometric2F1 -1 e p -1 2 c s c v d -1 n d -1 e p -1 2 c s c v d -1 -1 b d z a -1 e p 2 c s -1 c v z -1 e p -1 2 c s c v Hypergeometric2F1 e p 2 c s -1 c v d -1 n d e p 2 c s -1 c v d -1 -1 b d z a -1 -1 e -1 p -1 2 c s c v -1 e p -1 2 c s c v -1 e p -1 2 c s c v z -1 e p 2 c s -1 c v Hypergeometric2F1 e p -1 2 c s c v d -1 n d e p -1 2 c s c v d -1 -1 b d z a -1 -1 e p 2 c s -1 c v z -1 e -1 p 2 c s -1 c v Hypergeometric2F1 -1 e p 2 c s -1 c v d -1 n d -1 e p 2 c s -1 c v d -1 -1 b d z a -1 -1 e -1 p 2 c s -1 c v -1 e p 2 c s -1 c v -1 -1 2 -1 v -1 a -1 n e -1 p e p -1 Binomial v v 2 -1 -1 e p z e p Hypergeometric2F1 -1 e p d -1 n d -1 e p d -1 -1 b d z a -1 e p z e -1 p Hypergeometric2F1 e p d -1 n d e p d -1 -1 b d z a -1 1 -1 \$CellContext`v 2 n SuperPlus v SuperPlus [/itex]

 Rule Form

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

 2002-12-18