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Exp






Mathematica Notation

Traditional Notation









Elementary Functions > Exp[z] > Integration > Indefinite integration > Involving functions of the direct function > Involving algebraic functions of the direct function > Involving (a+b e2c z)beta(ec z)nu





http://functions.wolfram.com/01.03.21.0509.01









  


  










Input Form





Integrate[(a + b E^(2 c z))^(5/2) (E^(c z))^\[Nu], z] == ((E^(c z))^\[Nu] Sqrt[a + b E^(2 c z)] (2 a b E^(2 c z) \[Nu] (4 + \[Nu]) Hypergeometric2F1[-(1/2), 1 + \[Nu]/2, 2 + \[Nu]/2, -((b E^(2 c z))/a)] + (2 + \[Nu]) (b^2 E^(4 c z) \[Nu] Hypergeometric2F1[-(1/2), 2 + \[Nu]/2, 3 + \[Nu]/2, -((b E^(2 c z))/a)] + a^2 (4 + \[Nu]) Hypergeometric2F1[-(1/2), \[Nu]/2, 1 + \[Nu]/2, -((b E^(2 c z))/a)])))/ (c Sqrt[1 + (b E^(2 c z))/a] \[Nu] (2 + \[Nu]) (4 + \[Nu]))










Standard Form





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MathML Form







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Rule Form





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





2002-12-18





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