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Exp






Mathematica Notation

Traditional Notation









Elementary Functions > Exp[z] > Integration > Indefinite integration > Involving functions of the direct function and a power function > Involving products of the direct function and a power function > Involving products of two direct functions and a power function > Involving znab zr hc zr+f z+g





http://functions.wolfram.com/01.03.21.0608.01









  


  










Input Form





Integrate[z^n a^(b Sqrt[z]) h^(c Sqrt[z] + f z + g), z] == (2^(-1 - 2 n) h^g Sum[(-1)^(-j + k) 4^k Binomial[k, j] Binomial[n, k] (b Log[a] + c Log[h])^(-j - k + 2 n) (b Log[a] + c Log[h] + 2 f Sqrt[z] Log[h])^(j + k) (-((b Log[a] + c Log[h] + 2 f Sqrt[z] Log[h])^2/(f Log[h])))^ ((1/2) (-1 - j - k)) (Gamma[(1/2) (1 + j + k), -((b Log[a] + c Log[h] + 2 f Sqrt[z] Log[h])^2/(4 f Log[h]))] (b Log[a] + c Log[h]) (b Log[a] + c Log[h] + 2 f Sqrt[z] Log[h]) + 2 f Gamma[(1/2) (2 + j + k), -((b Log[a] + c Log[h] + 2 f Sqrt[z] Log[h])^2/(4 f Log[h]))] Log[h] Sqrt[-((b Log[a] + c Log[h] + 2 f Sqrt[z] Log[h])^2/(f Log[h]))]), {k, 0, n}, {j, 0, k}])/(E^((b Log[a] + c Log[h])^2/(4 f Log[h])) (f Log[h])^(2 (1 + n))) /; Element[n, Integers] && n >= 0










Standard Form





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MathML Form







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</ci> </apply> </apply> <apply> <times /> <ci> c </ci> <apply> <ln /> <ci> h </ci> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> f </ci> <apply> <ln /> <ci> h </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <ci> h </ci> <ci> g </ci> </apply> <apply> <power /> <apply> <times /> <ci> f </ci> <apply> <ln /> <ci> h </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -2 </cn> <apply> <plus /> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <apply> <sum /> <bvar> <ci> j </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> k </ci> </uplimit> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <apply> <plus /> <ci> k </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> </apply> </apply> <apply> <power /> <cn type='integer'> 4 </cn> <ci> k </ci> </apply> <apply> <ci> Binomial </ci> <ci> k </ci> <ci> j </ci> </apply> <apply> <ci> Binomial </ci> <ci> n </ci> <ci> k </ci> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> b </ci> <apply> <ln /> <ci> a </ci> </apply> </apply> <apply> <times /> <ci> c </ci> <apply> <ln /> <ci> h </ci> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> n </ci> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> b </ci> <apply> <ln /> <ci> a </ci> </apply> </apply> <apply> <times /> <ci> c </ci> <apply> <ln /> <ci> h </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> f </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ln /> <ci> h </ci> </apply> </apply> </apply> <apply> <plus /> <ci> j </ci> <ci> k </ci> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> b </ci> <apply> <ln /> <ci> a </ci> </apply> </apply> <apply> <times /> <ci> c </ci> <apply> <ln /> <ci> h </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> f </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ln /> <ci> h </ci> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <ci> f </ci> <apply> <ln /> <ci> h </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> f </ci> <apply> <ci> Gamma </ci> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <ci> j </ci> <ci> k </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> b </ci> <apply> <ln /> <ci> a </ci> </apply> </apply> <apply> <times /> <ci> c </ci> <apply> <ln /> <ci> h </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> f </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ln /> <ci> h </ci> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> f </ci> <apply> <ln /> <ci> h </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> b </ci> <apply> <ln /> <ci> a </ci> </apply> </apply> <apply> <times /> <ci> c </ci> <apply> <ln /> <ci> h </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> f </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ln /> <ci> h </ci> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <ci> f </ci> <apply> <ln /> <ci> h </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ln /> <ci> h </ci> </apply> </apply> <apply> <times /> <apply> <ci> Gamma </ci> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <ci> j </ci> <ci> k </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power 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Rule Form





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





2002-12-18