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 Cosh

 http://functions.wolfram.com/01.20.21.0607.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18