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 Cos

 http://functions.wolfram.com/01.07.21.2734.01

 Input Form

 Integrate[z^(\[Alpha] - 1) E^(b z^r + e) Sin[a z^r + q] Cos[c z^r + g]^v, z] == (-(1/r)) (2^(-1 - v) z^\[Alpha] ((-I) E^(e - I q) Binomial[v, v/2] ((E^(2 I q) Gamma[\[Alpha]/r, ((-I) a - b) z^r])/ (((-I) a - b) z^r)^(\[Alpha]/r) - Gamma[\[Alpha]/r, I (a + I b) z^r]/ (I (a + I b) z^r)^(\[Alpha]/r)) (1 - Mod[v, 2]) + Sum[(-I) E^(e - I (q + g (2 s + v))) Binomial[v, s] ((E^(2 I (q + 2 g s)) Gamma[\[Alpha]/r, (-I) (a - I b + 2 c s - c v) z^r])/((-I) (a - I b + 2 c s - c v) z^r)^(\[Alpha]/r) - (E^(2 I g v) Gamma[\[Alpha]/r, I (a + I b + 2 c s - c v) z^r])/ (I (a + I b + 2 c s - c v) z^r)^(\[Alpha]/r) + (E^(2 I (q + g v)) Gamma[\[Alpha]/r, (-I) (a - I b - 2 c s + c v) z^r])/((-I) (a - I b - 2 c s + c v) z^r)^(\[Alpha]/r) - (E^(4 I g s) Gamma[\[Alpha]/r, I (a + I b - 2 c s + c v) z^r])/ (I (a + I b - 2 c s + c v) z^r)^(\[Alpha]/r)), {s, 0, Floor[(1/2) (-1 + v)]}])) /; Element[v, Integers] && v > 0

 Standard Form

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"b"]], "-", RowBox[List["2", " ", "c", " ", "s"]], "+", RowBox[List["c", " ", "v"]]]], ")"]], " ", SuperscriptBox["z", "r"]]]]], "]"]]]]]], ")"]]]]]]]], ")"]]]], ")"]]]]]], "/;", RowBox[List[RowBox[List["v", "\[Element]", "Integers"]], "\[And]", RowBox[List["v", ">", "0"]]]]]]]]

 MathML Form

 z α - 1 b z r + e sin ( a z r + q ) cos v ( c z r + g ) z - 2 - v - 1 z α r ( s = 0 v - 1 2 - e - ( q + g ( 2 s + v ) ) ( v s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( - 4 g s Γ ( α r , ( a + b - 2 c s + c v ) z r ) ( ( a + b - 2 c s + c v ) z r ) - α r + 2 ( q + g v ) ( - ( a - b - 2 c s + c v ) z r ) - α r Γ ( α r , - ( a - b - 2 c s + c v ) z r ) - 2 g v ( ( a + b + 2 c s - c v ) z r ) - α r Γ ( α r , ( a + b + 2 c s - c v ) z r ) + 2 ( q + 2 g s ) ( - ( a - b + 2 c s - c v ) z r ) - α r Γ ( α r , - ( a - b + 2 c s - c v ) z r ) ) - e - q ( 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]]]]] ( 2 q ( ( - b - a ) z r ) - α r Γ ( α r , ( - b - a ) z r ) - ( ( a + b ) z r ) - α r Γ ( α r , ( a + b ) z r ) ) ( 1 - v mod 2 \$CellContext`v 2 ) ) /; v + Condition z z α -1 b z r e a z r q c z r g v -1 2 -1 v -1 z α r -1 s 0 v -1 2 -1 -1 e -1 q g 2 s v Binomial v s -1 4 g s Gamma α r -1 a b -1 2 c s c v z r a b -1 2 c s c v z r -1 α r -1 2 q g v -1 a -1 b -1 2 c s c v z r -1 α r -1 Gamma α r -1 -1 a -1 b -1 2 c s c v z r -1 2 g v a b 2 c s -1 c v z r -1 α r -1 Gamma α r -1 a b 2 c s -1 c v z r 2 q 2 g s -1 a -1 b 2 c s -1 c v z r -1 α r -1 Gamma α r -1 -1 a -1 b 2 c s -1 c v z r -1 e -1 q Binomial v v 2 -1 2 q -1 b -1 a z r -1 α r -1 Gamma α r -1 -1 b -1 a z r -1 a b z r -1 α r -1 Gamma α r -1 a b z r 1 -1 \$CellContext`v 2 v SuperPlus [/itex]

 Rule Form

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

 2002-12-18