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 Cosh

 http://functions.wolfram.com/01.20.21.4090.01

 Input Form

 Integrate[Sinh[d z + e] Cosh[c z^2 + f z]^v, z] == (Cosh[e + d z] Binomial[v, v/2] (1 - Mod[v, 2]))/(2^v d) + 2^(-2 - v) Sqrt[Pi] Sum[Binomial[v, s] ((E^(e + (d - 2 f s + f v)^2/(8 c s - 4 c v)) Erfi[(d - (2 s - v) (f + 2 c z))/(2 Sqrt[c (-2 s + v)])])/ Sqrt[c (-2 s + v)] + (E^(-e - (d - 2 f s + f v)^2/(8 c s - 4 c v)) Sqrt[2 c s - c v] Erfi[(-d + (2 s - v) (f + 2 c z))/ (2 Sqrt[2 c s - c v])])/(c (-2 s + v)) + (1/(2 c s - c v)) (E^(-e - (-d + f (-2 s + v))^2/(-8 c s + 4 c v)) (Sqrt[-2 c s + c v] Erfi[(-d - (2 s - v) (f + 2 c z))/ (2 Sqrt[-2 c s + c v])] + E^(2 (e + (-d - 2 f s + f v)^2/(-8 c s + 4 c v))) Sqrt[2 c s - c v] Erfi[(d + (2 s - v) (f + 2 c z))/(2 Sqrt[2 c s - c v])]))), {s, 0, Floor[(1/2) (-1 + v)]}] /; Element[v, Integers] && v > 0

 Standard Form

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")"]]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]]]]]]]], "]"]]]]]], ")"]]]], ")"]]]]]], ")"]]]]]]]]]]]], "/;", RowBox[List[RowBox[List["v", "\[Element]", "Integers"]], "\[And]", RowBox[List["v", ">", "0"]]]]]]]]

 MathML Form

 sinh ( e + d z ) cosh v ( c z 2 + f z ) z 2 - v ( v v 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox[FractionBox["v", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] cosh ( e + d z ) ( 1 - v mod 2 \$CellContext`v 2 ) d + 2 - v - 2 π s = 0 v - 1 2 ( v s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( ( d - 2 f s + f v ) 2 8 c s - 4 c v + e erfi ( d - ( 2 s - v ) ( f + 2 c z ) 2 c ( v - 2 s ) ) c ( v - 2 s ) + - ( d - 2 f s + f v ) 2 8 c s - 4 c v - e 2 c s - c v erfi ( ( 2 s - v ) ( f + 2 c z ) - d 2 2 c s - c v ) c ( v - 2 s ) + 1 2 c s - c v ( - ( f ( v - 2 s ) - d ) 2 4 c v - 8 c s - e ( c v - 2 c s erfi ( - d - ( 2 s - v ) ( f + 2 c z ) 2 c v - 2 c s ) + 2 ( ( - d - 2 f s + f v ) 2 4 c v - 8 c s + e ) 2 c s - c v erfi ( d + ( 2 s - v ) ( f + 2 c z ) 2 2 c s - c v ) ) ) ) /; v + Condition z e d z c z 2 f z v 2 -1 v Binomial v v 2 -1 e d z 1 -1 \$CellContext`v 2 d -1 2 -1 v -2 1 2 s 0 v -1 2 -1 Binomial v s d -1 2 f s f v 2 8 c s -1 4 c v -1 e Erfi d -1 2 s -1 v f 2 c z 2 c v -1 2 s 1 2 -1 c v -1 2 s 1 2 -1 -1 d -1 2 f s f v 2 8 c s -1 4 c v -1 -1 e 2 c s -1 c v 1 2 Erfi 2 s -1 v f 2 c z -1 d 2 2 c s -1 c v 1 2 -1 c v -1 2 s -1 1 2 c s -1 c v -1 -1 f v -1 2 s -1 d 2 4 c v -1 8 c s -1 -1 e c v -1 2 c s 1 2 Erfi -1 d -1 2 s -1 v f 2 c z 2 c v -1 2 c s 1 2 -1 2 -1 d -1 2 f s f v 2 4 c v -1 8 c s -1 e 2 c s -1 c v 1 2 Erfi d 2 s -1 v f 2 c z 2 2 c s -1 c v 1 2 -1 v SuperPlus [/itex]

 Rule Form

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

 2002-12-18