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 Cosh

 http://functions.wolfram.com/01.20.21.1214.01

 Input Form

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

 Standard Form

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 MathML Form

 p z sin m ( d + c z ) cosh ( b + a z ) z ( m m 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox[FractionBox["m", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] p z ( m mod 2 \$CellContext`m 2 - 1 ) ( p cosh ( b + a z ) - a sinh ( b + a z ) ) ( a 2 - p 2 ) 2 m + 2 1 - m k = 0 m - 1 2 ( - 1 ) k p z ( m k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( cos ( 2 d k - d m + m π 2 ) ( c ( 2 k - m ) sin ( c ( m - 2 k ) z ) ( ( - a 2 - c 2 ( m - 2 k ) 2 - p 2 ) cosh ( b + a z ) + 2 a p sinh ( b + a z ) ) - cos ( c ( m - 2 k ) z ) ( p ( a 2 - c 2 ( m - 2 k ) 2 - p 2 ) cosh ( b + a z ) + a ( - a 2 - c 2 ( m - 2 k ) 2 + p 2 ) sinh ( b + a z ) ) ) - sin ( 2 d k - d m + m π 2 ) ( c ( 2 k - m ) cos ( c ( m - 2 k ) z ) ( ( - a 2 - c 2 ( m - 2 k ) 2 - p 2 ) cosh ( b + a z ) + 2 a p sinh ( b + a z ) ) + sin ( c ( m - 2 k ) z ) ( p ( a 2 - c 2 ( m - 2 k ) 2 - p 2 ) cosh ( b + a z ) + a ( - a 2 - c 2 ( m - 2 k ) 2 + p 2 ) sinh ( b + a z ) ) ) ) / ( a 4 + 2 ( c 2 ( m - 2 k ) 2 - p 2 ) a 2 + ( c 2 ( m - 2 k ) 2 + p 2 ) 2 ) /; m + Condition z p z d c z m b a z Binomial m m 2 -1 p z \$CellContext`m 2 -1 p b a z -1 a b a z a 2 -1 p 2 2 m -1 2 1 -1 m k 0 m -1 2 -1 -1 k p z Binomial m k 2 d k -1 d m m 2 -1 c 2 k -1 m c m -1 2 k z -1 a 2 -1 c 2 m -1 2 k 2 -1 p 2 b a z 2 a p b a z -1 c m -1 2 k z p a 2 -1 c 2 m -1 2 k 2 -1 p 2 b a z a -1 a 2 -1 c 2 m -1 2 k 2 p 2 b a z -1 2 d k -1 d m m 2 -1 c 2 k -1 m c m -1 2 k z -1 a 2 -1 c 2 m -1 2 k 2 -1 p 2 b a z 2 a p b a z c m -1 2 k z p a 2 -1 c 2 m -1 2 k 2 -1 p 2 b a z a -1 a 2 -1 c 2 m -1 2 k 2 p 2 b a z a 4 2 c 2 m -1 2 k 2 -1 p 2 a 2 c 2 m -1 2 k 2 p 2 2 -1 m SuperPlus [/itex]

 Rule Form

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

 2002-12-18