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 Cosh

 http://functions.wolfram.com/01.20.21.1556.01

 Input Form

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

 Standard Form

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RowBox[List["(", RowBox[List["d", "+", RowBox[List["2", " ", "b", " ", "z"]]]], ")"]]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]]]]]], "]"]]]], SqrtBox[RowBox[List["b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]]]]]], ")"]]]]]]]]]]]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Integers"]], "\[And]", RowBox[List["m", ">", "0"]]]]]]]]

 MathML Form

 sinh m ( b z 2 + d z ) cosh ( c 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 ( c z ) ( 2 ) m c + 2 - m - 2 π 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 - 2 d k + d m ) 2 8 b k - 4 b m erfi ( c - 2 k ( d + 2 b z ) + m ( d + 2 b z ) 2 b ( m - 2 k ) ) b ( m - 2 k ) + 1 b m - 2 b k ( - ( c + 2 d k - d m ) 2 8 b k - 4 b m ( ( c + 2 d k - d m ) 2 4 b k - 2 b m b m - 2 b k erfi ( - c - 2 k ( d + 2 b z ) + m ( d + 2 b z ) 2 b m - 2 b k ) - ( - 1 ) m 2 b k - b m erfi ( c + 2 k ( d + 2 b z ) - m ( d + 2 b z ) 2 2 b k - b m ) ) ) - ( - 1 ) m - ( c - 2 d k + d m ) 2 8 b k - 4 b m 2 b k - b m erfi ( - c + 2 k ( d + 2 b z ) - m ( d + 2 b z ) 2 2 b k - b m ) b ( m - 2 k ) ) /; m + Condition z b z 2 d z m c z Binomial m m 2 -1 1 -1 \$CellContext`m 2 c z 2 -1 m c -1 2 -1 m -2 1 2 k 0 m -1 2 -1 -1 k Binomial m k c -1 2 d k d m 2 8 b k -1 4 b m -1 Erfi c -1 2 k d 2 b z m d 2 b z 2 b m -1 2 k 1 2 -1 b m -1 2 k 1 2 -1 1 b m -1 2 b k -1 -1 c 2 d k -1 d m 2 8 b k -1 4 b m -1 c 2 d k -1 d m 2 4 b k -1 2 b m -1 b m -1 2 b k 1 2 Erfi -1 c -1 2 k d 2 b z m d 2 b z 2 b m -1 2 b k 1 2 -1 -1 -1 m 2 b k -1 b m 1 2 Erfi c 2 k d 2 b z -1 m d 2 b z 2 2 b k -1 b m 1 2 -1 -1 -1 m -1 c -1 2 d k d m 2 8 b k -1 4 b m -1 2 b k -1 b m 1 2 Erfi -1 c 2 k d 2 b z -1 m d 2 b z 2 2 b k -1 b m 1 2 -1 b 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