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 Cos

 http://functions.wolfram.com/01.07.21.2425.01

 Input Form

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

 Standard Form

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 MathML Form

 z α - 1 sin ( c z ) cos v ( b + a z ) z 2 - v - 1 z α ( ( 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]] ( ( c z ) α Γ ( α , - c z ) - ( - c z ) α Γ ( α , c z ) ) ( 1 - v mod 2 \$CellContext`v 2 ) ( c 2 z 2 ) - α + s = 0 v - 1 2 - ( 2 b s + b v ) ( ( c + 2 a s - a v ) 2 z 2 ) - α ( ( c - 2 a s + a v ) 2 z 2 ) - α ( 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]] ( 4 b s ( ( c + 2 a s - a v ) z ) α Γ ( α , - ( c + 2 a s - a v ) z ) ( ( c - 2 a s + a v ) 2 z 2 ) α - 2 b v ( - ( c + 2 a s - a v ) z ) α Γ ( α , ( c + 2 a s - a v ) z ) ( ( c - 2 a s + a v ) 2 z 2 ) α + ( ( c + 2 a s - a v ) 2 z 2 ) α ( 2 b v ( ( c - 2 a s + a v ) z ) α Γ ( α , - ( c - 2 a s + a v ) z ) - 4 b s ( - ( c - 2 a s + a v ) z ) α Γ ( α , ( c - 2 a s + a v ) z ) ) ) ) /; v + Condition z z α -1 c z b a z v 2 -1 v -1 z α Binomial v v 2 -1 c z α Gamma α -1 c z -1 -1 c z α Gamma α c z 1 -1 \$CellContext`v 2 c 2 z 2 -1 α s 0 v -1 2 -1 -1 2 b s b v c 2 a s -1 a v 2 z 2 -1 α c -1 2 a s a v 2 z 2 -1 α Binomial v s 4 b s c 2 a s -1 a v z α Gamma α -1 c 2 a s -1 a v z c -1 2 a s a v 2 z 2 α -1 2 b v -1 c 2 a s -1 a v z α Gamma α c 2 a s -1 a v z c -1 2 a s a v 2 z 2 α c 2 a s -1 a v 2 z 2 α 2 b v c -1 2 a s a v z α Gamma α -1 c -1 2 a s a v z -1 4 b s -1 c -1 2 a s a v z α Gamma α c -1 2 a s a v z v SuperPlus [/itex]

 Rule Form

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

 2002-12-18