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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/01.03.21.0791.01









  


  










Input Form





Integrate[z^3/(a E^(2 d z) + b E^(d z) + c), z] == (-(1/(2 Sqrt[b^2 - 4 a c]))) (a (z^4/(-b + Sqrt[b^2 - 4 a c]) + z^4/(b + Sqrt[b^2 - 4 a c]) + (4 z^3 Log[1 + (2 a E^(d z))/(b - Sqrt[b^2 - 4 a c])])/ ((b - Sqrt[b^2 - 4 a c]) d) - (4 z^3 Log[1 + (2 a E^(d z))/(b + Sqrt[b^2 - 4 a c])])/ ((b + Sqrt[b^2 - 4 a c]) d) + (12 z^2 PolyLog[2, (2 a E^(d z))/(-b + Sqrt[b^2 - 4 a c])])/ ((b - Sqrt[b^2 - 4 a c]) d^2) - (12 z^2 PolyLog[2, -((2 a E^(d z))/(b + Sqrt[b^2 - 4 a c]))])/ ((b + Sqrt[b^2 - 4 a c]) d^2) + (24 z PolyLog[3, (2 a E^(d z))/(-b + Sqrt[b^2 - 4 a c])])/ ((-b + Sqrt[b^2 - 4 a c]) d^3) + (24 z PolyLog[3, -((2 a E^(d z))/(b + Sqrt[b^2 - 4 a c]))])/ ((b + Sqrt[b^2 - 4 a c]) d^3) + (24 PolyLog[4, (2 a E^(d z))/(-b + Sqrt[b^2 - 4 a c])])/ ((b - Sqrt[b^2 - 4 a c]) d^4) - (24 PolyLog[4, -((2 a E^(d z))/(b + Sqrt[b^2 - 4 a c]))])/ ((b + Sqrt[b^2 - 4 a c]) d^4)))










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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