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/01.20.21.4603.01

 Input Form

 Integrate[(z Sinh[2 c z])/(a Sinh[c z] + b Cosh[c z])^2, z] == (1/(a (a + b))) ((a^2 z^2)/(a b - b^2) + (2 a^2 (a c z - b Log[b Cosh[c z] + a Sinh[c z]]))/ ((a - b)^2 (a + b) c^2) + (a^2 (((-c^2) z^2)/E^ArcTanh[b/a] + (1/(a Sqrt[1 - b^2/a^2])) (b (I (c Pi z - Pi Log[1 + E^(2 c z)] - 2 I c z Log[1 - E^(-2 (c z + ArcTanh[b/a]))] + Pi Log[Cosh[c z]]) + 2 ArcTanh[b/a] (c z + Log[1 - E^(-2 (c z + ArcTanh[b/a]))] - Log[I Sinh[c z + ArcTanh[b/a]]]) - PolyLog[2, E^(-2 (c z + ArcTanh[b/a]))]))))/((a - b) b Sqrt[1 - b^2/a^2] c^2) - (b (((-c^2) z^2)/E^ArcTanh[b/a] + (1/(a Sqrt[1 - b^2/a^2])) (b (I (c Pi z - Pi Log[1 + E^(2 c z)] - 2 I c z Log[1 - E^(-2 (c z + ArcTanh[b/a]))] + Pi Log[Cosh[c z]]) + 2 ArcTanh[b/a] (c z + Log[1 - E^(-2 (c z + ArcTanh[b/a]))] - Log[I Sinh[c z + ArcTanh[b/a]]]) - PolyLog[2, E^(-2 (c z + ArcTanh[b/a]))]))))/((-a + b) Sqrt[1 - b^2/a^2] c^2) + (2 a^2 z Sinh[c z])/((-a + b) c (b Cosh[c z] + a Sinh[c z])))

 Standard Form

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")"]]]]]]], "]"]]]], ")"]]]], ")"]]]]]], ")"]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b"]], ")"]], " ", SqrtBox[RowBox[List["1", "-", FractionBox[SuperscriptBox["b", "2"], SuperscriptBox["a", "2"]]]]], " ", SuperscriptBox["c", "2"]]], ")"]]]], "+", FractionBox[RowBox[List["2", " ", SuperscriptBox["a", "2"], " ", "z", " ", RowBox[List["Sinh", "[", RowBox[List["c", " ", "z"]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b"]], ")"]], " ", "c", " ", RowBox[List["(", RowBox[List[RowBox[List["b", " ", RowBox[List["Cosh", "[", RowBox[List["c", " ", "z"]], "]"]]]], "+", RowBox[List["a", " ", RowBox[List["Sinh", "[", RowBox[List["c", " ", "z"]], "]"]]]]]], ")"]]]]]]], ")"]]]]]]]]

 MathML Form

 z sinh ( 2 c z ) ( a sinh ( c z ) + b cosh ( c z ) ) 2 z 1 a ( a + b ) ( z 2 a 2 a b - b 2 + 2 ( a c z - b log ( b cosh ( c z ) + a sinh ( c z ) ) ) a 2 ( a - b ) 2 ( a + b ) c 2 + 2 z sinh ( c z ) a 2 ( b - a ) c ( b cosh ( c z ) + a sinh ( c z ) ) + a 2 ( a - b ) b 1 - b 2 a 2 c 2 ( b a 1 - b 2 a 2 ( ( - 2 c log ( 1 - - 2 ( c z + tanh - 1 ( b a ) ) ) z + c π z - π log ( 1 + 2 c z ) + π log ( cosh ( c z ) ) ) + 2 tanh - 1 ( b a ) ( c z + log ( 1 - - 2 ( c z + tanh - 1 ( b a ) ) ) - log ( sinh ( c z + tanh - 1 ( b a ) ) ) ) - Li PolyLog 2 ( - 2 ( c z + tanh - 1 ( b a ) ) ) ) - c 2 - tanh - 1 ( b a ) z 2 ) - b ( b - a ) 1 - b 2 a 2 c 2 ( b a 1 - b 2 a 2 ( ( - 2 c log ( 1 - - 2 ( c z + tanh - 1 ( b a ) ) ) z + c π z - π log ( 1 + 2 c z ) + π log ( cosh ( c z ) ) ) + 2 tanh - 1 ( b a ) ( c z + log ( 1 - - 2 ( c z + tanh - 1 ( b a ) ) ) - log ( sinh ( c z + tanh - 1 ( b a ) ) ) ) - Li PolyLog 2 ( - 2 ( c z + tanh - 1 ( b a ) ) ) ) - c 2 - tanh - 1 ( b a ) z 2 ) ) z z 2 c z a c z b c z 2 -1 1 a a b -1 z 2 a 2 a b -1 b 2 -1 2 a c z -1 b b c z a c z a 2 a -1 b 2 a b c 2 -1 2 z c z a 2 b -1 a c b c z a c z -1 a 2 a -1 b b 1 -1 b 2 a 2 -1 1 2 c 2 -1 b a 1 -1 b 2 a 2 -1 1 2 -1 -2 c 1 -1 -2 c z b a -1 z c z -1 1 2 c z c z 2 b a -1 c z 1 -1 -2 c z b a -1 -1 c z b a -1 -1 PolyLog 2 -2 c z b a -1 -1 c 2 -1 b a -1 z 2 -1 b b -1 a 1 -1 b 2 a 2 -1 1 2 c 2 -1 b a 1 -1 b 2 a 2 -1 1 2 -1 -2 c 1 -1 -2 c z b a -1 z c z -1 1 2 c z c z 2 b a -1 c z 1 -1 -2 c z b a -1 -1 c z b a -1 -1 PolyLog 2 -2 c z b a -1 -1 c 2 -1 b a -1 z 2 [/itex]

 Rule Form

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

 2002-12-18