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 Cosh

 http://functions.wolfram.com/01.20.21.1282.01

 Input Form

 Integrate[E^(p z) Cos[c z]^m Cosh[a z], z] == (1/(p^2 - a^2)) ((E^(p z) Binomial[m, m/2] (1 - Mod[m, 2]) (p Cosh[a z] - a Sinh[a z]))/2^m) + 2^(1 - m) E^(p z) Sum[Binomial[m, k] ((Cosh[a z] (p (-a^2 + c^2 (-2 k + m)^2 + p^2) Cos[c (2 k - m) z] + c (2 k - m) (a^2 + c^2 (-2 k + m)^2 + p^2) Sin[c (2 k - m) z]) + a ((a^2 + c^2 (-2 k + m)^2 - p^2) Cos[c (2 k - m) z] + 2 c (-2 k + m) p Sin[c (2 k - m) z]) Sinh[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 cos m ( c z ) cosh ( 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]]]]] 2 - m p z ( 1 - m mod 2 \$CellContext`m 2 ) ( p cosh ( a z ) - a sinh ( a z ) ) p 2 - a 2 + 2 1 - m p z k = 0 m - 1 2 ( m k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( cosh ( a z ) ( p ( - a 2 + p 2 + c 2 ( m - 2 k ) 2 ) cos ( c ( 2 k - m ) z ) + ( a 2 + p 2 + c 2 ( m - 2 k ) 2 ) c ( 2 k - m ) sin ( c ( 2 k - m ) z ) ) + a ( ( a 2 - p 2 + c 2 ( m - 2 k ) 2 ) cos ( c ( 2 k - m ) z ) + 2 p c ( m - 2 k ) sin ( c ( 2 k - m ) z ) ) sinh ( a z ) ) / ( a 4 + 2 ( c 2 ( m - 2 k ) 2 - p 2 ) a 2 + ( p 2 + c 2 ( m - 2 k ) 2 ) 2 ) /; m + Condition z p z c z m a z Binomial m m 2 -1 2 -1 m p z 1 -1 \$CellContext`m 2 p a z -1 a a z p 2 -1 a 2 -1 2 1 -1 m p z k 0 m -1 2 -1 Binomial m k a z p -1 a 2 p 2 c 2 m -1 2 k 2 c 2 k -1 m z a 2 p 2 c 2 m -1 2 k 2 c 2 k -1 m c 2 k -1 m z a a 2 -1 p 2 c 2 m -1 2 k 2 c 2 k -1 m z 2 p c m -1 2 k c 2 k -1 m z a z a 4 2 c 2 m -1 2 k 2 -1 p 2 a 2 p 2 c 2 m -1 2 k 2 2 -1 m SuperPlus [/itex]

 Rule Form

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

 2002-12-18