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 Cosh

 http://functions.wolfram.com/01.20.21.1231.01

 Input Form

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

 Standard Form

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 MathML Form

 b z 2 + e sin m ( a z 2 + q ) cosh ( c z 2 + g ) z 2 - m - 2 ( erfi ( b - c z ) b - c + 2 g erfi ( b + c z ) b + c ) e - g π ( 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 ) + 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]]]]] ( e - g + ( m - 2 k ) q - m π 2 ( erfi ( b - c + a ( m - 2 k ) z ) b - c + a ( m - 2 k ) + 2 ( g - ( m - 2 k ) q + m π 2 ) erfi ( b + c - a ( m - 2 k ) z ) b + c - a ( m - 2 k ) ) + e - g - ( m - 2 k ) q + m π 2 ( 2 ( g + ( m - 2 k ) q - m π 2 ) erfi ( b + c + a ( m - 2 k ) z ) b + c + a ( m - 2 k ) + erfi ( b - c - a ( m - 2 k ) z ) b - c - a ( m - 2 k ) ) ) /; m + Condition z b z 2 e a z 2 q m c z 2 g 2 -1 m -2 Erfi b -1 c 1 2 z b -1 c 1 2 -1 2 g Erfi b c 1 2 z b c 1 2 -1 e -1 g 1 2 Binomial m m 2 -1 1 -1 \$CellContext`m 2 2 -1 m -2 1 2 k 0 m -1 2 -1 -1 k Binomial m k e -1 g m -1 2 k q -1 m 2 -1 Erfi b -1 c a m -1 2 k 1 2 z b -1 c a m -1 2 k 1 2 -1 2 g -1 m -1 2 k q m 2 -1 Erfi b c -1 a m -1 2 k 1 2 z b c -1 a m -1 2 k 1 2 -1 e -1 g -1 m -1 2 k q m 2 -1 2 g m -1 2 k q -1 m 2 -1 Erfi b c a m -1 2 k 1 2 z b c a m -1 2 k 1 2 -1 Erfi b -1 c -1 a m -1 2 k 1 2 z b -1 c -1 a m -1 2 k 1 2 -1 m SuperPlus [/itex]

 Rule Form

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

 2002-12-18