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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 rational functions of the direct function and a power function > Involving zn/a e2d z+b ed z+c





http://functions.wolfram.com/01.03.21.0790.01









  


  










Input Form





Integrate[z^2/(a E^(2 d z) + b E^(d z) + c), z] == (2 Sqrt[b^2 - 4 a c] d^3 z^3 - 3 b d^2 z^2 Log[1 + (2 a E^(d z))/(b - Sqrt[b^2 - 4 a c])] - 3 Sqrt[b^2 - 4 a c] d^2 z^2 Log[1 + (2 a E^(d z))/(b - Sqrt[b^2 - 4 a c])] + 3 b d^2 z^2 Log[1 + (2 a E^(d z))/(b + Sqrt[b^2 - 4 a c])] - 3 Sqrt[b^2 - 4 a c] d^2 z^2 Log[1 + (2 a E^(d z))/(b + Sqrt[b^2 - 4 a c])] - 6 (b + Sqrt[b^2 - 4 a c]) d z PolyLog[2, (2 a E^(d z))/ (-b + Sqrt[b^2 - 4 a c])] + 6 (b - Sqrt[b^2 - 4 a c]) d z PolyLog[2, -((2 a E^(d z))/(b + Sqrt[b^2 - 4 a c]))] + 6 b PolyLog[3, (2 a E^(d z))/(-b + Sqrt[b^2 - 4 a c])] + 6 Sqrt[b^2 - 4 a c] PolyLog[3, (2 a E^(d z))/(-b + Sqrt[b^2 - 4 a c])] - 6 b PolyLog[3, -((2 a E^(d z))/(b + Sqrt[b^2 - 4 a c]))] + 6 Sqrt[b^2 - 4 a c] PolyLog[3, -((2 a E^(d z))/(b + Sqrt[b^2 - 4 a c]))])/ (6 c Sqrt[b^2 - 4 a c] d^3)










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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