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Exp




Mathematica Notation

Traditional Notation









Elementary Functions > Exp[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Arguments involving polynomials or algebraic functions and power factors > Involving power > Involving zn da zr+b z+c





http://functions.wolfram.com/01.03.21.0213.01









  


  








Input Form





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








Standard Form





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MathML Form







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</cn> <ci> b </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <ln /> <ci> d </ci> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> b </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <ln /> <ci> d </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> n </ci> <ci> &#8469; </ci> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2002-12-18