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 Cosh

 http://functions.wolfram.com/01.20.21.1547.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18