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 Cos

 http://functions.wolfram.com/01.07.21.2717.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18