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 Cos

 http://functions.wolfram.com/01.07.21.2450.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18