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Sech






Mathematica Notation

Traditional Notation









Elementary Functions > Sech[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving power function > Involving power > Involving znand linear arguments





http://functions.wolfram.com/01.24.21.0030.01









  


  










Input Form





Integrate[z^3 Sech[a z], z] == (1/(64 a^4)) (I (-7 Pi^4 - 8 I a Pi^3 z - 24 a^2 Pi^2 z^2 + 32 I a^3 Pi z^3 + 16 a^4 z^4 - 8 I Pi^3 Log[1 + I/E^(a z)] - 48 a Pi^2 z Log[1 + I/E^(a z)] + 96 I a^2 Pi z^2 Log[1 + I/E^(a z)] + 64 a^3 z^3 Log[1 + I/E^(a z)] + 48 a Pi^2 z Log[1 - I E^(a z)] - 96 I a^2 Pi z^2 Log[1 - I E^(a z)] + 8 I Pi^3 Log[1 + I E^(a z)] - 64 a^3 z^3 Log[1 + I E^(a z)] - 8 I Pi^3 Log[Cot[(1/4) (Pi - 2 I a z)]] + 48 (Pi - 2 I a z)^2 PolyLog[2, -I/E^(a z)] - 192 a^2 z^2 PolyLog[2, (-I) E^(a z)] + 48 Pi^2 PolyLog[2, I E^(a z)] - 192 I a Pi z PolyLog[2, I E^(a z)] - 192 I Pi PolyLog[3, -I/E^(a z)] - 384 a z PolyLog[3, -I/E^(a z)] + 384 a z PolyLog[3, (-I) E^(a z)] + 192 I Pi PolyLog[3, I E^(a z)] - 384 PolyLog[4, -I/E^(a z)] - 384 PolyLog[4, (-I) E^(a z)]))










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