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 Cos

 http://functions.wolfram.com/01.07.21.2598.01

 Input Form

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

 Standard Form

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 MathML Form

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