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 Cos

 http://functions.wolfram.com/01.07.21.2581.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18