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 Cosh

 http://functions.wolfram.com/01.20.21.3753.01

 Input Form

 Integrate[E^(b Sqrt[z] + d z + e) Sin[a Sqrt[z] + p z + q] Cosh[c Sqrt[z] + f z + g]^v, z] == 2^(-2 - v) E^(e + (I Pi)/2 - I q) Binomial[v, v/2] ((2 E^(((-I) a + b) Sqrt[z] + (d - I p) z))/(d - I p) - (2 E^(2 I q + (I a + b) Sqrt[z] + (d + I p) z))/(d + I p) + Sqrt[Pi] (-((((-I) a + b) Erfi[((-I) a + b + 2 (d - I p) Sqrt[z])/ (2 Sqrt[d - I p])])/(E^(((-I) a + b)^2/(4 (d - I p))) (d - I p)^(3/2))) + ((I a + b) E^(-((I a + b)^2/(4 (d + I p))) + 2 I q) Erfi[(I a + b + 2 (d + I p) Sqrt[z])/(2 Sqrt[d + I p])])/ (d + I p)^(3/2))) (1 - Mod[v, 2]) + 2^(-2 - v) Sum[Binomial[v, s] (E^(e - (I Pi)/2 + I q - g (-2 s + v)) ((2 E^((I a + b + 2 c s - c v) Sqrt[z] + (d + I p + 2 f s - f v) z))/ (d + I p + 2 f s - f v) - (2 E^(-2 I q + 2 g (-2 s + v) + ((-I) a + b - 2 c s + c v) Sqrt[z] + (d - I p - 2 f s + f v) z))/ (d - I p - 2 f s + f v) - (Sqrt[Pi] (I a + b + 2 c s - c v) Erfi[(I a + b + c (2 s - v) + 2 (d + I p + 2 f s - f v) Sqrt[z])/ (2 Sqrt[d + I p + 2 f s - f v])])/E^((I a + b + 2 c s - c v)^2/ (4 (d + I p + 2 f s - f v)))/(d + I p + 2 f s - f v)^(3/2) + (E^(-2 I q + 2 g (-2 s + v) - ((-I) a + b - 2 c s + c v)^2/ (4 (d - I p - 2 f s + f v))) Sqrt[Pi] ((-I) a + b - 2 c s + c v) Erfi[((-I) a + b + c (-2 s + v) + 2 (d - I p - 2 f s + f v) Sqrt[z])/(2 Sqrt[d - I p - 2 f s + f v])])/ (d - I p - 2 f s + f v)^(3/2)) + E^(e + (I Pi)/2 - I q - g (-2 s + v)) ((2 E^(((-I) a + b + 2 c s - c v) Sqrt[z] + (d - I p + 2 f s - f v) z))/(d - I p + 2 f s - f v) - (2 E^(2 I q + 2 g (-2 s + v) + (I a + b - 2 c s + c v) Sqrt[z] + (d + I p - 2 f s + f v) z))/(d + I p - 2 f s + f v) - (Sqrt[Pi] ((-I) a + b + 2 c s - c v) Erfi[((-I) a + b + c (2 s - v) + 2 (d - I p + 2 f s - f v) Sqrt[z])/(2 Sqrt[d - I p + 2 f s - f v])])/ E^(((-I) a + b + 2 c s - c v)^2/(4 (d - I p + 2 f s - f v)))/ (d - I p + 2 f s - f v)^(3/2) + (E^(2 I q + 2 g (-2 s + v) - (I a + b + c (-2 s + v))^2/ (4 (d + I p - 2 f s + f v))) Sqrt[Pi] (I a + b + c (-2 s + v)) Erfi[(I a + b + c (-2 s + v) + 2 (d + I p - 2 f s + f v) Sqrt[z])/ (2 Sqrt[d + I p - 2 f s + f v])])/(d + I p - 2 f s + f v)^ (3/2))), {s, 0, Floor[(1/2) (-1 + v)]}] /; Element[v, Integers] && v > 0

 Standard Form

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 MathML Form

 z b + d z + e sin ( z a + p z + q ) cosh v ( z c + f z + g ) z 2 - v - 2 e - q + π 2 ( π ( ( b + a ) 2 q - ( b + a ) 2 4 ( d + p ) erfi ( b + a + 2 ( d + p ) z 2 d + p ) ( d + p ) 3 / 2 - ( b - a ) - ( b - a ) 2 4 ( d - p ) erfi ( b - a + 2 ( d - p ) z 2 d - p ) ( d - p ) 3 / 2 ) - 2 z ( b + a ) + 2 q + ( d + p ) z d + p + 2 z ( b - a ) + ( d - p ) z d - p ) ( 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]]]]] ( 1 - v mod 2 \$CellContext`v 2 ) + 2 - v - 2 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]]]]] ( e - q - g ( v - 2 s ) + π 2 ( 1 ( d + p - 2 f s + f v ) 3 / 2 ( - ( b + a + c ( v - 2 s ) ) 2 4 ( d + p - 2 f s + f v ) + 2 q + 2 g ( v - 2 s ) π ( b + a + c ( v - 2 s ) ) erfi ( b + a + c ( v - 2 s ) + 2 ( d + p - 2 f s + f v ) z 2 d + p - 2 f s + f v ) ) - 2 2 q + 2 g ( v - 2 s ) + ( d + p - 2 f s + f v ) z + ( b + a - 2 c s + c v ) z d + p - 2 f s + f v + 2 z ( b - a + 2 c s - c v ) + ( d - p + 2 f s - f v ) z d - p + 2 f s - f v - ( - ( b - a + 2 c s - c v ) 2 4 ( d - p + 2 f s - f v ) π ( b - a + 2 c s - c v ) erfi ( b - a + c ( 2 s - v ) + 2 ( d - p + 2 f s - f v ) z 2 d - p + 2 f s - f v ) ) / ( d - p + 2 f s - f v ) 3 / 2 ) + e + q - g ( v - 2 s ) - π 2 ( 1 ( d - p - 2 f s + f v ) 3 / 2 ( - ( b - a - 2 c s + c v ) 2 4 ( d - p - 2 f s + f v ) - 2 q + 2 g ( v - 2 s ) π ( b - a - 2 c s + c v ) erfi ( b - a + c ( v - 2 s ) + 2 ( d - p - 2 f s + f v ) z 2 d - p - 2 f s + f v ) ) - 2 - 2 q + 2 g ( v - 2 s ) + ( d - p - 2 f s + f v ) z + ( b - a - 2 c s + c v ) z d - p - 2 f s + f v + 2 z ( b + a + 2 c s - c v ) + ( d + p + 2 f s - f v ) z d + p + 2 f s - f v - ( - ( b + a + 2 c s - c v ) 2 4 ( d + p + 2 f s - f v ) π ( b + a + 2 c s - c v ) erfi ( b + a + c ( 2 s - v ) + 2 ( d + p + 2 f s - f v ) z 2 d + p + 2 f s - f v ) ) / ( d + p + 2 f s - f v ) 3 / 2 ) ) /; v + Condition z z 1 2 b d z e z 1 2 a p z q z 1 2 c f z g v 2 -1 v -2 e -1 q 2 -1 1 2 b a 2 q -1 b a 2 4 d p -1 Erfi b a 2 d p z 1 2 2 d p 1 2 -1 d p 3 2 -1 -1 b -1 a -1 b -1 a 2 4 d -1 p -1 Erfi b -1 a 2 d -1 p z 1 2 2 d -1 p 1 2 -1 d -1 p 3 2 -1 -1 2 z 1 2 b a 2 q d p z d p -1 2 z 1 2 b -1 a d -1 p z d -1 p -1 Binomial v v 2 -1 1 -1 \$CellContext`v 2 2 -1 v -2 s 0 v -1 2 -1 Binomial v s e -1 q -1 g v -1 2 s 2 -1 1 d p -1 2 f s f v 3 2 -1 -1 b a c v -1 2 s 2 4 d p -1 2 f s f v -1 2 q 2 g v -1 2 s 1 2 b a c v -1 2 s Erfi b a c v -1 2 s 2 d p -1 2 f s f v z 1 2 2 d p -1 2 f s f v 1 2 -1 -1 2 2 q 2 g v -1 2 s d p -1 2 f s f v z b a -1 2 c s c v z 1 2 d p -1 2 f s f v -1 2 z 1 2 b -1 a 2 c s -1 c v d -1 p 2 f s -1 f v z d -1 p 2 f s -1 f v -1 -1 -1 b -1 a 2 c s -1 c v 2 4 d -1 p 2 f s -1 f v -1 1 2 b -1 a 2 c s -1 c v Erfi b -1 a c 2 s -1 v 2 d -1 p 2 f s -1 f v z 1 2 2 d -1 p 2 f s -1 f v 1 2 -1 d -1 p 2 f s -1 f v 3 2 -1 e q -1 g v -1 2 s -1 2 -1 1 d -1 p -1 2 f s f v 3 2 -1 -1 b -1 a -1 2 c s c v 2 4 d -1 p -1 2 f s f v -1 -1 2 q 2 g v -1 2 s 1 2 b -1 a -1 2 c s c v Erfi b -1 a c v -1 2 s 2 d -1 p -1 2 f s f v z 1 2 2 d -1 p -1 2 f s f v 1 2 -1 -1 2 -2 q 2 g v -1 2 s d -1 p -1 2 f s f v z b -1 a -1 2 c s c v z 1 2 d -1 p -1 2 f s f v -1 2 z 1 2 b a 2 c s -1 c v d p 2 f s -1 f v z d p 2 f s -1 f v -1 -1 -1 b a 2 c s -1 c v 2 4 d p 2 f s -1 f v -1 1 2 b a 2 c s -1 c v Erfi b a c 2 s -1 v 2 d p 2 f s -1 f v z 1 2 2 d p 2 f s -1 f v 1 2 -1 d p 2 f s -1 f v 3 2 -1 v SuperPlus [/itex]

 Rule Form

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

 2002-12-18