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http://functions.wolfram.com/01.03.21.0518.01
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Integrate[Sqrt[a E^(2 d z) + b E^(d z) + c], z] ==
(1/(2 d)) (2 Sqrt[c + b E^(d z) + a E^(2 d z)] -
2 Sqrt[c] Log[(d (2 c + b E^(d z) + 2 Sqrt[c]
Sqrt[c + b E^(d z) + a E^(2 d z)]))/(E^(d z) c^(3/2))] +
(b Log[(b + 2 a E^(d z))/Sqrt[a] + 2 Sqrt[c + E^(d z) (b + a E^(d z))]])/
Sqrt[a])
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<power /> <exponentiale /> <apply> <times /> <ci> d </ci> <ci> z </ci> </apply> </apply> </apply> <ci> c </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <ci> b </ci> <apply> <power /> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ln /> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <ci> d </ci> <ci> z </ci> </apply> </apply> <ci> a </ci> </apply> <ci> b </ci> </apply> <apply> <power /> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> c </ci> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <ci> d </ci> <ci> z </ci> 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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[SqrtBox[RowBox[List[RowBox[List["a_", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "d_", " ", "z_"]]]]], "+", RowBox[List["b_", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["d_", " ", "z_"]]]]], "+", "c_"]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["2", " ", SqrtBox[RowBox[List["c", "+", RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["d", " ", "z"]]]]], "+", RowBox[List["a", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "d", " ", "z"]]]]]]]]]], "-", RowBox[List["2", " ", SqrtBox["c"], " ", RowBox[List["Log", "[", FractionBox[RowBox[List["d", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "d"]], " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "c"]], "+", RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["d", " ", "z"]]]]], "+", RowBox[List["2", " ", SqrtBox["c"], " ", SqrtBox[RowBox[List["c", "+", RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["d", " ", "z"]]]]], "+", RowBox[List["a", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "d", " ", "z"]]]]]]]]]]]], ")"]]]], SuperscriptBox["c", RowBox[List["3", "/", "2"]]]], "]"]]]], "+", FractionBox[RowBox[List["b", " ", RowBox[List["Log", "[", RowBox[List[FractionBox[RowBox[List["b", "+", RowBox[List["2", " ", "a", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["d", " ", "z"]]]]]]], SqrtBox["a"]], "+", RowBox[List["2", " ", SqrtBox[RowBox[List["c", "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["d", " ", "z"]]], " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["a", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["d", " ", "z"]]]]]]], ")"]]]]]]]]]]], "]"]]]], SqrtBox["a"]]]], RowBox[List["2", " ", "d"]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
