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 Cosh

 http://functions.wolfram.com/01.20.21.3799.01

 Input Form

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

 Standard Form

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 MathML Form

 p z cos ( c z ) cosh v ( a z + b ) z - 2 - v - 1 ( 2 p z ( p cos ( c z ) + c sin ( c z ) ) ( v mod 2 \$CellContext`v 2 - 1 ) c 2 + p 2 ( 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]]]]] + s = 0 v - 1 2 - b ( 2 s + v ) ( - 4 b s + ( c + p + 2 a s - a v ) z c + p + 2 a s - a v - 2 b v + ( c + p - 2 a s + a v ) z c + p - 2 a s + a v + 2 b v + ( - c + p - 2 a s + a v ) z c - p + 2 a s - a v + 4 b s + ( - c + p + 2 a s - a v ) z c - p + a ( v - 2 s ) ) ( 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 c z a z b v -1 2 -1 v -1 2 p z p c z c c z \$CellContext`v 2 -1 c 2 p 2 -1 Binomial v v 2 -1 s 0 v -1 2 -1 -1 b 2 s v -1 4 b s c p 2 a s -1 a v z c p 2 a s -1 a v -1 -1 2 b v c p -1 2 a s a v z c p -1 2 a s a v -1 2 b v -1 c p -1 2 a s a v z c -1 p 2 a s -1 a v -1 4 b s -1 c p 2 a s -1 a v z c -1 p a v -1 2 s -1 Binomial v s v SuperPlus [/itex]

 Rule Form

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

 2002-12-18