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 Cosh

 http://functions.wolfram.com/01.20.21.1563.01

 Input Form

 Integrate[Sinh[b Sqrt[z] + e]^m Cosh[f z + g], z] == ((I/2)^m Binomial[m, m/2] (1 - Mod[m, 2]) Sinh[g + f z])/f + 2^(-2 - m) Sum[(-1)^k Binomial[m, k] (E^(-g - e (2 k - m)) (-((2 E^((-b) (2 k - m) Sqrt[z] - f z))/f) + (2 (-1)^m E^(2 (g + e (2 k - m)) + b (2 k - m) Sqrt[z] + f z))/f - (b E^((b^2 (2 k - m)^2)/(4 f)) (2 k - m) Sqrt[Pi] Erfi[(b (2 k - m) + 2 f Sqrt[z])/(2 Sqrt[-f])])/(-f)^(3/2) - (1/f^(3/2)) ((-1)^m b E^(2 (g + e (2 k - m)) - (b^2 (2 k - m)^2)/ (4 f)) (2 k - m) Sqrt[Pi] Erfi[(b (2 k - m) + 2 f Sqrt[z])/ (2 Sqrt[f])])) + (-1)^m E^(-g - e (-2 k + m)) (-((2 E^((-b) (-2 k + m) Sqrt[z] - f z))/f) + (2 (-1)^m E^(2 (g + e (-2 k + m)) + b (-2 k + m) Sqrt[z] + f z))/f - (b E^((b^2 (-2 k + m)^2)/(4 f)) (-2 k + m) Sqrt[Pi] Erfi[(b (-2 k + m) + 2 f Sqrt[z])/(2 Sqrt[-f])])/(-f)^(3/2) - (1/f^(3/2)) ((-1)^m b E^(-((b^2 (-2 k + m)^2)/(4 f)) + 2 (g + e (-2 k + m))) (-2 k + m) Sqrt[Pi] Erfi[(b (-2 k + m) + 2 f Sqrt[z])/(2 Sqrt[f])]))), {k, 0, Floor[(1/2) (-1 + m)]}] /; Element[m, Integers] && m > 0

 Standard Form

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RowBox[List["2", " ", SqrtBox["f"]]]], "]"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]]]]]]]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Integers"]], "\[And]", RowBox[List["m", ">", "0"]]]]]]]]

 MathML Form

 sinh m ( z b + e ) cosh ( g + f 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 ( g + f z ) ( 2 ) m f + 2 - m - 2 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]]]]] ( - g - e ( 2 k - m ) ( - b b 2 ( 2 k - m ) 2 4 f ( 2 k - m ) π erfi ( 2 z f + b ( 2 k - m ) 2 - f ) ( - f ) 3 / 2 - ( - 1 ) m b 2 ( g + e ( 2 k - m ) ) - b 2 ( 2 k - m ) 2 4 f ( 2 k - m ) π erfi ( 2 z f + b ( 2 k - m ) 2 f ) f 3 / 2 + 2 ( - 1 ) m 2 ( g + e ( 2 k - m ) ) + f z + b ( 2 k - m ) z f - 2 - b z ( 2 k - m ) - f z f ) + ( - 1 ) m - g - e ( m - 2 k ) ( - b b 2 ( m - 2 k ) 2 4 f ( m - 2 k ) π erfi ( 2 z f + b ( m - 2 k ) 2 - f ) ( - f ) 3 / 2 - ( - 1 ) m b 2 ( g + e ( m - 2 k ) ) - b 2 ( m - 2 k ) 2 4 f ( m - 2 k ) π erfi ( 2 z f + b ( m - 2 k ) 2 f ) f 3 / 2 + 2 ( - 1 ) m b z ( m - 2 k ) + 2 ( g + e ( m - 2 k ) ) + f z f - 2 - b z ( m - 2 k ) - f z f ) ) /; m + Condition z z 1 2 b e m g f z Binomial m m 2 -1 1 -1 \$CellContext`m 2 g f z 2 -1 m f -1 2 -1 m -2 k 0 m -1 2 -1 -1 k Binomial m k -1 g -1 e 2 k -1 m -1 b b 2 2 k -1 m 2 4 f -1 2 k -1 m 1 2 Erfi 2 z 1 2 f b 2 k -1 m 2 -1 f 1 2 -1 -1 f 3 2 -1 -1 -1 m b 2 g e 2 k -1 m -1 b 2 2 k -1 m 2 4 f -1 2 k -1 m 1 2 Erfi 2 z 1 2 f b 2 k -1 m 2 f 1 2 -1 f 3 2 -1 2 -1 m 2 g e 2 k -1 m f z b 2 k -1 m z 1 2 f -1 -1 2 -1 b z 1 2 2 k -1 m -1 f z f -1 -1 m -1 g -1 e m -1 2 k -1 b b 2 m -1 2 k 2 4 f -1 m -1 2 k 1 2 Erfi 2 z 1 2 f b m -1 2 k 2 -1 f 1 2 -1 -1 f 3 2 -1 -1 -1 m b 2 g e m -1 2 k -1 b 2 m -1 2 k 2 4 f -1 m -1 2 k 1 2 Erfi 2 z 1 2 f b m -1 2 k 2 f 1 2 -1 f 3 2 -1 2 -1 m b z 1 2 m -1 2 k 2 g e m -1 2 k f z f -1 -1 2 -1 b z 1 2 m -1 2 k -1 f z f -1 m SuperPlus [/itex]

 Rule Form

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

 2002-12-18