|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
http://functions.wolfram.com/01.03.21.0254.01
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Integrate[(E^(c Sqrt[z^2]))^v, z] == ((E^(c Sqrt[z^2]))^v Sqrt[z^2])/(c v z)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox[RowBox[List["(", SuperscriptBox["\[ExponentialE]", RowBox[List["c", " ", SqrtBox[SuperscriptBox["z", "2"]]]]], ")"]], "v"], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", SuperscriptBox["\[ExponentialE]", RowBox[List["c", " ", SqrtBox[SuperscriptBox["z", "2"]]]]], ")"]], "v"], " ", SqrtBox[SuperscriptBox["z", "2"]]]], RowBox[List["c", " ", "v", " ", "z"]]]]]]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mo> ∫ </mo> <mrow> <msup> <mrow> <mo> ( </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> c </mi> <mo> ⁢ </mo> <msqrt> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </msqrt> </mrow> </msup> <mo> ) </mo> </mrow> <mi> v </mi> </msup> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mfrac> <mrow> <msup> <mrow> <mo> ( </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> c </mi> <mo> ⁢ </mo> <msqrt> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </msqrt> </mrow> </msup> <mo> ) </mo> </mrow> <mi> v </mi> </msup> <mo> ⁢ </mo> <msqrt> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </msqrt> </mrow> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> v </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <power /> <apply> <power /> <exponentiale /> <apply> <times /> <ci> c </ci> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <ci> v </ci> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <power /> <exponentiale /> <apply> <times /> <ci> c </ci> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <ci> v </ci> </apply> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <times /> <ci> c </ci> <ci> v </ci> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
|
|
|
|
|
|
|
|
|
|
| |
|
|
|
|
| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[SuperscriptBox[RowBox[List["(", SuperscriptBox["\[ExponentialE]", RowBox[List["c_", " ", SqrtBox[SuperscriptBox["z_", "2"]]]]], ")"]], "v_"], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", SuperscriptBox["\[ExponentialE]", RowBox[List["c", " ", SqrtBox[SuperscriptBox["z", "2"]]]]], ")"]], "v"], " ", SqrtBox[SuperscriptBox["z", "2"]]]], RowBox[List["c", " ", "v", " ", "z"]]]]]]] |
|
|
|
|
|
|
|
|
|
|
Date Added to functions.wolfram.com (modification date)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|