html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 Cosh

 http://functions.wolfram.com/01.20.21.1239.01

 Input Form

 Integrate[E^(p z) Sin[a z] Sin[b z] Cosh[c z], z] == (-(1/4)) E^(p z) (((-p) Cos[(a - b - I c) z] + (-a + b + I c) Sin[(a - b - I c) z])/(a^2 + b^2 - 2 a (b + I c) + 2 I b c - c^2 + p^2) + (p Cos[(a + b - I c) z] + (a + b - I c) Sin[(a + b - I c) z])/((a + b - I (c - p)) (a + b - I (c + p))) + ((-p) Cos[(a - b + I c) z] + (-a + b - I c) Sin[(a - b + I c) z])/((a - b + I (c - p)) (a - b + I (c + p))) + (p Cos[(a + b + I c) z] + (a + b + I c) Sin[(a + b + I c) z])/((a + b + I (c - p)) (a + b + I (c + p))))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["p", " ", "z"]]], RowBox[List["Sin", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["Sin", "[", RowBox[List["b", " ", "z"]], "]"]], " ", RowBox[List["Cosh", "[", RowBox[List["c", " ", "z"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox["1", "4"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["p", " ", "z"]]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "p"]], " ", RowBox[List["Cos", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b", "-", RowBox[List["\[ImaginaryI]", " ", "c"]]]], ")"]], " ", "z"]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["\[ImaginaryI]", " ", "c"]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b", "-", RowBox[List["\[ImaginaryI]", " ", "c"]]]], ")"]], " ", "z"]], "]"]]]]]], RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", RowBox[List["2", " ", "a", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "c"]]]], ")"]]]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "c"]], "-", SuperscriptBox["c", "2"], "+", SuperscriptBox["p", "2"]]]], "+", FractionBox[RowBox[List[RowBox[List["p", " ", RowBox[List["Cos", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b", "-", RowBox[List["\[ImaginaryI]", " ", "c"]]]], ")"]], " ", "z"]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b", "-", RowBox[List["\[ImaginaryI]", " ", "c"]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b", "-", RowBox[List["\[ImaginaryI]", " ", "c"]]]], ")"]], " ", "z"]], "]"]]]]]], RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b", "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["c", "-", "p"]], ")"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List["a", "+", "b", "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["c", "+", "p"]], ")"]]]]]], ")"]]]]], "+", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "p"]], " ", RowBox[List["Cos", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b", "+", RowBox[List["\[ImaginaryI]", " ", "c"]]]], ")"]], " ", "z"]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "-", RowBox[List["\[ImaginaryI]", " ", "c"]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b", "+", RowBox[List["\[ImaginaryI]", " ", "c"]]]], ")"]], " ", "z"]], "]"]]]]]], RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b", "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["c", "-", "p"]], ")"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List["a", "-", "b", "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["c", "+", "p"]], ")"]]]]]], ")"]]]]], "+", FractionBox[RowBox[List[RowBox[List["p", " ", RowBox[List["Cos", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["\[ImaginaryI]", " ", "c"]]]], ")"]], " ", "z"]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["\[ImaginaryI]", " ", "c"]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["\[ImaginaryI]", " ", "c"]]]], ")"]], " ", "z"]], "]"]]]]]], RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["c", "-", "p"]], ")"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["c", "+", "p"]], ")"]]]]]], ")"]]]]]]], ")"]]]]]]]]

 MathML Form

 p z sin ( a z ) sin ( b z ) cosh ( c z ) z - 1 4 p z ( ( - a + b - c ) sin ( ( a - b + c ) z ) - p cos ( ( a - b + c ) z ) ( a - b + ( c - p ) ) ( a - b + ( c + p ) ) + p cos ( ( a + b + c ) z ) + ( a + b + c ) sin ( ( a + b + c ) z ) ( a + b + ( c - p ) ) ( a + b + ( c + p ) ) + ( - a + b + c ) sin ( ( a - b - c ) z ) - p cos ( ( a - b - c ) z ) a 2 - 2 ( b + c ) a + b 2 - c 2 + p 2 + 2 b c + p cos ( ( a + b - c ) z ) + ( a + b - c ) sin ( ( a + b - c ) z ) ( a + b - ( c - p ) ) ( a + b - ( c + p ) ) ) z p z a z b z c z -1 1 4 p z -1 a b -1 c a -1 b c z -1 p a -1 b c z a -1 b c -1 p a -1 b c p -1 p a b c z a b c a b c z a b c -1 p a b c p -1 -1 a b c a -1 b -1 c z -1 p a -1 b -1 c z a 2 -1 2 b c a b 2 -1 c 2 p 2 2 b c -1 p a b -1 c z a b -1 c a b -1 c z a b -1 c -1 p a b -1 c p -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["p_", " ", "z_"]]], " ", RowBox[List["Sin", "[", RowBox[List["a_", " ", "z_"]], "]"]], " ", RowBox[List["Sin", "[", RowBox[List["b_", " ", "z_"]], "]"]], " ", RowBox[List["Cosh", "[", RowBox[List["c_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", FractionBox["1", "4"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["p", " ", "z"]]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "p"]], " ", RowBox[List["Cos", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b", "-", RowBox[List["\[ImaginaryI]", " ", "c"]]]], ")"]], " ", "z"]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", RowBox[List["\[ImaginaryI]", " ", "c"]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b", "-", RowBox[List["\[ImaginaryI]", " ", "c"]]]], ")"]], " ", "z"]], "]"]]]]]], RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"], "-", RowBox[List["2", " ", "a", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "c"]]]], ")"]]]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "c"]], "-", SuperscriptBox["c", "2"], "+", SuperscriptBox["p", "2"]]]], "+", FractionBox[RowBox[List[RowBox[List["p", " ", RowBox[List["Cos", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b", "-", RowBox[List["\[ImaginaryI]", " ", "c"]]]], ")"]], " ", "z"]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b", "-", RowBox[List["\[ImaginaryI]", " ", "c"]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b", "-", RowBox[List["\[ImaginaryI]", " ", "c"]]]], ")"]], " ", "z"]], "]"]]]]]], RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b", "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["c", "-", "p"]], ")"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List["a", "+", "b", "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["c", "+", "p"]], ")"]]]]]], ")"]]]]], "+", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "p"]], " ", RowBox[List["Cos", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b", "+", RowBox[List["\[ImaginaryI]", " ", "c"]]]], ")"]], " ", "z"]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b", "-", RowBox[List["\[ImaginaryI]", " ", "c"]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b", "+", RowBox[List["\[ImaginaryI]", " ", "c"]]]], ")"]], " ", "z"]], "]"]]]]]], RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b", "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["c", "-", "p"]], ")"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List["a", "-", "b", "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["c", "+", "p"]], ")"]]]]]], ")"]]]]], "+", FractionBox[RowBox[List[RowBox[List["p", " ", RowBox[List["Cos", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["\[ImaginaryI]", " ", "c"]]]], ")"]], " ", "z"]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["\[ImaginaryI]", " ", "c"]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["\[ImaginaryI]", " ", "c"]]]], ")"]], " ", "z"]], "]"]]]]]], RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["c", "-", "p"]], ")"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["c", "+", "p"]], ")"]]]]]], ")"]]]]]]], ")"]]]]]]]]

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

 2002-12-18