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 Cosh

 http://functions.wolfram.com/01.20.21.1208.01

 Input Form

 Integrate[E^(p z) Sin[c z]^m Cosh[a z], z] == (1/(a^2 - p^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) Sum[((-1)^k E^(p z) Binomial[m, k] ((-Cosh[a z]) (Cos[c (-2 k + m) z] (p (a^2 - p^2 - c^2 (-2 k + m)^2) Cos[(m Pi)/2] - c (2 k - m) (a^2 + p^2 + c^2 (-2 k + m)^2) Sin[(m Pi)/2]) + (c (2 k - m) (a^2 + p^2 + c^2 (-2 k + m)^2) Cos[(m Pi)/2] + p (a^2 - p^2 - c^2 (-2 k + m)^2) Sin[(m Pi)/2]) Sin[c (-2 k + m) z]) + a ((-Cos[c (-2 k + m) z]) ((-a^2 + p^2 - c^2 (-2 k + m)^2) Cos[(m Pi)/2] + 2 p c (2 k - m) Sin[(m Pi)/2]) - (-2 p c (2 k - m) Cos[(m Pi)/2] + (-a^2 + p^2 - c^2 (-2 k + m)^2) Sin[(m Pi)/2]) Sin[c (-2 k + m) z]) Sinh[a z]))/ (a^4 - 2 a^2 (p^2 - c^2 (-2 k + m)^2) + (p^2 + c^2 (-2 k + m)^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 ( 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 ) ( a sinh ( a z ) - p cosh ( a z ) ) a 2 - p 2 + 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]]]]] ( a ( - cos ( c ( m - 2 k ) z ) ( ( - a 2 + p 2 - c 2 ( m - 2 k ) 2 ) cos ( m π 2 ) + 2 p c ( 2 k - m ) sin ( m π 2 ) ) - ( ( - a 2 + p 2 - c 2 ( m - 2 k ) 2 ) sin ( m π 2 ) - 2 p c ( 2 k - m ) cos ( m π 2 ) ) sin ( c ( m - 2 k ) z ) ) sinh ( a z ) - cosh ( a z ) ( cos ( c ( m - 2 k ) z ) ( p ( a 2 - p 2 - c 2 ( m - 2 k ) 2 ) cos ( m π 2 ) - c ( 2 k - m ) ( a 2 + p 2 + c 2 ( m - 2 k ) 2 ) sin ( m π 2 ) ) + ( c ( 2 k - m ) ( a 2 + p 2 + c 2 ( m - 2 k ) 2 ) cos ( m π 2 ) + p ( a 2 - p 2 - c 2 ( m - 2 k ) 2 ) sin ( m π 2 ) ) sin ( c ( m - 2 k ) z ) ) ) / ( a 4 - 2 ( p 2 - c 2 ( m - 2 k ) 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 a a z -1 p a z a 2 -1 p 2 -1 2 1 -1 m k 0 m -1 2 -1 -1 k p z Binomial m k a -1 c m -1 2 k z -1 a 2 p 2 -1 c 2 m -1 2 k 2 m 2 -1 2 p c 2 k -1 m m 2 -1 -1 -1 a 2 p 2 -1 c 2 m -1 2 k 2 m 2 -1 -1 2 p c 2 k -1 m m 2 -1 c m -1 2 k z a z -1 a z c m -1 2 k z p a 2 -1 p 2 -1 c 2 m -1 2 k 2 m 2 -1 -1 c 2 k -1 m a 2 p 2 c 2 m -1 2 k 2 m 2 -1 c 2 k -1 m a 2 p 2 c 2 m -1 2 k 2 m 2 -1 p a 2 -1 p 2 -1 c 2 m -1 2 k 2 m 2 -1 c m -1 2 k z a 4 -1 2 p 2 -1 c 2 m -1 2 k 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