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http://functions.wolfram.com/01.03.21.0043.01
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Integrate[a^(b (z^r)^p), z] == -((z Gamma[1/(p r), (-b) Log[a] (z^r)^p])/
(((-b) Log[a] (z^r)^p)^(1/(p r)) (p r)))
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Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["a", RowBox[List["b", " ", SuperscriptBox[RowBox[List["(", SuperscriptBox["z", "r"], ")"]], "p"]]]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List["-", FractionBox[RowBox[List["z", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], " ", RowBox[List["Log", "[", "a", " ", "]"]], SuperscriptBox[RowBox[List["(", SuperscriptBox["z", "r"], ")"]], "p"]]], ")"]], RowBox[List["-", FractionBox["1", RowBox[List["p", " ", "r"]]]]]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", RowBox[List["p", " ", "r"]]], ",", RowBox[List[RowBox[List["-", "b"]], " ", RowBox[List["Log", "[", "a", "]"]], " ", SuperscriptBox[RowBox[List["(", SuperscriptBox["z", "r"], ")"]], "p"]]]]], "]"]]]], RowBox[List["p", " ", "r"]]]]]]]]]
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<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> <mi> a </mi> <mrow> <mi> b </mi> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> <mo> ) </mo> </mrow> <mi> p </mi> </msup> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> z </mi> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> b </mi> </mrow> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> <mo> ) </mo> </mrow> <mi> p </mi> </msup> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mrow> <mi> p </mi> <mo> ⁢ </mo> <mi> r </mi> </mrow> </mfrac> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mi> p </mi> <mo> ⁢ </mo> <mi> r </mi> </mrow> </mfrac> <mo> , </mo> <mrow> <mrow> <mo> - </mo> <mi> b </mi> </mrow> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> <mo> ) </mo> </mrow> <mi> p </mi> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mi> p </mi> <mo> ⁢ </mo> <mi> r </mi> </mrow> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <power /> <ci> a </ci> <apply> <times /> <ci> b </ci> <apply> <power /> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> <ci> p </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> z </ci> <apply> <power /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <ln /> <ci> a </ci> </apply> <apply> <power /> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> <ci> p </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <ci> p </ci> <ci> r </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <ci> p </ci> <ci> r </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <ln /> <ci> a </ci> </apply> <apply> <power /> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> <ci> p </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <ci> p </ci> <ci> r </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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Date Added to functions.wolfram.com (modification date)
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