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/01.20.21.0160.01

 Input Form

 Integrate[(a z + b)^(3/2) Cosh[c z], z] == (1/(2 a)) (((b + a z)^(5/2) (-((1/(-((c (b + a z))/a))^(5/2)) (E^(c (b/a + z)) (-((c (b + a z))/a))^(3/2) + (3/4) (Sqrt[Pi] + 2 E^(c (b/a + z)) Sqrt[-((c (b + a z))/a)] - Sqrt[Pi] Erf[Sqrt[-((c (b + a z))/a)]]))) - (1/((c (b + a z))/a)^(5/2)) (E^((2 b c)/a) (((c (b + a z))/a)^(3/2)/E^(c (b/a + z)) + (3/2) (Sqrt[(c (b + a z))/a]/E^(c (b/a + z)) - (1/2) Sqrt[Pi] (-1 + Erf[Sqrt[(c (b + a z))/a]]))))))/E^((b c)/a))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["a", " ", "z"]], "+", "b"]], ")"]], RowBox[List["3", "/", "2"]]], RowBox[List["Cosh", "[", RowBox[List["c", " ", "z"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["2", " ", "a"]]], RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List["b", " ", "c"]], "a"]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], ")"]], RowBox[List["5", "/", "2"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List[FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[RowBox[List["c", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], ")"]]]], "a"]]], ")"]], RowBox[List["5", "/", "2"]]]], RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["c", " ", RowBox[List["(", RowBox[List[FractionBox["b", "a"], "+", "z"]], ")"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[RowBox[List["c", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], ")"]]]], "a"]]], ")"]], RowBox[List["3", "/", "2"]]]]], "+", RowBox[List[FractionBox["3", "4"], " ", RowBox[List["(", RowBox[List[SqrtBox["\[Pi]"], "+", RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["c", " ", RowBox[List["(", RowBox[List[FractionBox["b", "a"], "+", "z"]], ")"]]]]], " ", SqrtBox[RowBox[List["-", FractionBox[RowBox[List["c", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], ")"]]]], "a"]]]]]], "-", RowBox[List[SqrtBox["\[Pi]"], " ", RowBox[List["Erf", "[", SqrtBox[RowBox[List["-", FractionBox[RowBox[List["c", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], ")"]]]], "a"]]]], "]"]]]]]], ")"]]]]]], ")"]]]]]], "-", RowBox[List[FractionBox["1", SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["c", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], ")"]]]], "a"], ")"]], RowBox[List["5", "/", "2"]]]], RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["2", " ", "b", " ", "c"]], "a"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "c"]], " ", RowBox[List["(", RowBox[List[FractionBox["b", "a"], "+", "z"]], ")"]]]]], " ", SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["c", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], ")"]]]], "a"], ")"]], RowBox[List["3", "/", "2"]]]]], "+", RowBox[List[FractionBox["3", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "c"]], " ", RowBox[List["(", RowBox[List[FractionBox["b", "a"], "+", "z"]], ")"]]]]], " ", SqrtBox[FractionBox[RowBox[List["c", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], ")"]]]], "a"]]]], "-", RowBox[List[FractionBox["1", "2"], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["Erf", "[", SqrtBox[FractionBox[RowBox[List["c", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], ")"]]]], "a"]], "]"]]]], ")"]]]]]], ")"]]]]]], ")"]]]], ")"]]]]]], ")"]]]], ")"]]]]]]]]

 MathML Form

 ( b + a z ) 3 / 2 cosh ( c z ) z 1 2 a ( - b c a ( b + a z ) 5 / 2 ( - 1 ( c ( b + a z ) a ) 5 / 2 ( 2 b c a ( - c ( b a + z ) ( c ( b + a z ) a ) 3 / 2 + 3 2 ( - c ( b a + z ) c ( b + a z ) a - 1 2 π ( erf ( c ( b + a z ) a ) - 1 ) ) ) ) - 1 ( - c ( b + a z ) a ) 5 / 2 ( c ( b a + z ) ( - c ( b + a z ) a ) 3 / 2 + 3 4 ( - π erf ( - c ( b + a z ) a ) + 2 - c ( b + a z ) a c ( b a + z ) + π ) ) ) ) z b a z 3 2 c z 1 2 a -1 -1 b c a -1 b a z 5 2 -1 1 c b a z a -1 5 2 -1 2 b c a -1 -1 c b a -1 z c b a z a -1 3 2 3 2 -1 c b a -1 z c b a z a -1 1 2 -1 1 2 1 2 Erf c b a z a -1 1 2 -1 -1 1 -1 c b a z a -1 5 2 -1 c b a -1 z -1 c b a z a -1 3 2 3 4 -1 1 2 Erf -1 c b a z a -1 1 2 2 -1 c b a z a -1 1 2 c b a -1 z 1 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["a_", " ", "z_"]], "+", "b_"]], ")"]], RowBox[List["3", "/", "2"]]], " ", RowBox[List["Cosh", "[", RowBox[List["c_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List["b", " ", "c"]], "a"]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], ")"]], RowBox[List["5", "/", "2"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["c", " ", RowBox[List["(", RowBox[List[FractionBox["b", "a"], "+", "z"]], ")"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[RowBox[List["c", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], ")"]]]], "a"]]], ")"]], RowBox[List["3", "/", "2"]]]]], "+", RowBox[List[FractionBox["3", "4"], " ", RowBox[List["(", RowBox[List[SqrtBox["\[Pi]"], "+", RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["c", " ", RowBox[List["(", RowBox[List[FractionBox["b", "a"], "+", "z"]], ")"]]]]], " ", SqrtBox[RowBox[List["-", FractionBox[RowBox[List["c", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], ")"]]]], "a"]]]]]], "-", RowBox[List[SqrtBox["\[Pi]"], " ", RowBox[List["Erf", "[", SqrtBox[RowBox[List["-", FractionBox[RowBox[List["c", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], ")"]]]], "a"]]]], "]"]]]]]], ")"]]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox[RowBox[List["c", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], ")"]]]], "a"]]], ")"]], RowBox[List["5", "/", "2"]]]]]], "-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["2", " ", "b", " ", "c"]], "a"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "c"]], " ", RowBox[List["(", RowBox[List[FractionBox["b", "a"], "+", "z"]], ")"]]]]], " ", SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["c", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], ")"]]]], "a"], ")"]], RowBox[List["3", "/", "2"]]]]], "+", RowBox[List[FractionBox["3", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "c"]], " ", RowBox[List["(", RowBox[List[FractionBox["b", "a"], "+", "z"]], ")"]]]]], " ", SqrtBox[FractionBox[RowBox[List["c", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], ")"]]]], "a"]]]], "-", RowBox[List[FractionBox["1", "2"], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["Erf", "[", SqrtBox[FractionBox[RowBox[List["c", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], ")"]]]], "a"]], "]"]]]], ")"]]]]]], ")"]]]]]], ")"]]]], SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["c", " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], ")"]]]], "a"], ")"]], RowBox[List["5", "/", "2"]]]]]], ")"]]]], RowBox[List["2", " ", "a"]]]]]]]

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

 2002-12-18