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 Cos

 http://functions.wolfram.com/01.07.21.2713.01

 Input Form

 Integrate[z^(\[Alpha] - 1) E^(p z) Sin[d + c z] Cos[a z]^v, z] == 2^(-1 - v) z^\[Alpha] I ((-E^((-I) d)) Binomial[v, v/2] (-ExpIntegralE[1 - \[Alpha], (I c - p) z] + E^(2 I d) ExpIntegralE[1 - \[Alpha], I (-c + I p) z]) (-1 + Mod[v, 2]) + Sum[(Binomial[v, s] (-ExpIntegralE[1 - \[Alpha], (-I) (-c - I p + 2 a s - a v) z] + E^(2 I d) ExpIntegralE[1 - \[Alpha], I (-c + I p + 2 a s - a v) z] - ExpIntegralE[1 - \[Alpha], (-I) (-c - I p - 2 a s + a v) z] + E^(2 I d) ExpIntegralE[1 - \[Alpha], I (-c + I p - 2 a s + a v) z]))/ E^(I d), {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 ( d + c z ) cos v ( a z ) z 2 - v - 1 z α ( s = 0 v - 1 2 - d ( v s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 2 d E TagBox["E", ExpIntegralE] 1 - α ( ( - c + p - 2 a s + a v ) z ) - E TagBox["E", ExpIntegralE] 1 - α ( - ( - c - p - 2 a s + a v ) z ) + 2 d E TagBox["E", ExpIntegralE] 1 - α ( ( - c + p + 2 a s - a v ) z ) - E TagBox["E", ExpIntegralE] 1 - α ( - ( - c - p + 2 a s - a v ) z ) ) - - 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 ( ( p - c ) z ) - E TagBox["E", ExpIntegralE] 1 - α ( ( c - p ) z ) ) ( v mod 2 \$CellContext`v 2 - 1 ) ) /; v + Condition z z α -1 p z d c z a z v 2 -1 v -1 z α s 0 v -1 2 -1 -1 d Binomial v s 2 d ExpIntegralE 1 -1 α -1 c p -1 2 a s a v z -1 ExpIntegralE 1 -1 α -1 -1 c -1 p -1 2 a s a v z 2 d ExpIntegralE 1 -1 α -1 c p 2 a s -1 a v z -1 ExpIntegralE 1 -1 α -1 -1 c -1 p 2 a s -1 a v z -1 -1 d Binomial v v 2 -1 2 d ExpIntegralE 1 -1 α p -1 c z -1 ExpIntegralE 1 -1 α c -1 p z \$CellContext`v 2 -1 v SuperPlus [/itex]

 Rule Form

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

 2002-12-18