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Cos






Mathematica Notation

Traditional Notation









Elementary Functions > Cos[z] > Integration > Indefinite integration > Involving functions of the direct function > Involving algebraic functions of the direct function > Involving ((a+b cos(c z))nu)beta cos(d z)





http://functions.wolfram.com/01.07.21.1311.01









  


  










Input Form





Integrate[((a + b Cos[c z])^\[Nu])^\[Beta] Cos[d z], z] == -((I (a + ((1/2) b (1 + E^(2 I c z)))/E^(I c z))^(\[Beta] \[Nu]) (E^(2 I d z) (d + c \[Beta] \[Nu]) AppellF1[d/c - \[Beta] \[Nu], (-\[Beta]) \[Nu], (-\[Beta]) \[Nu], 1 + d/c - \[Beta] \[Nu], -((b E^(I c z))/(a + Sqrt[a^2 - b^2])), (b E^(I c z))/ (-a + Sqrt[a^2 - b^2])] + (-d + c \[Beta] \[Nu]) AppellF1[-((d + c \[Beta] \[Nu])/c), (-\[Beta]) \[Nu], (-\[Beta]) \[Nu], 1 - d/c - \[Beta] \[Nu], -((b E^(I c z))/(a + Sqrt[a^2 - b^2])), (b E^(I c z))/ (-a + Sqrt[a^2 - b^2])]) ((a + b Cos[c z])^\[Nu])^\[Beta])/ (E^(I d z) (1 + (b E^(I c z))/(a - Sqrt[a^2 - b^2]))^(\[Beta] \[Nu]) (1 + (b E^(I c z))/(a + Sqrt[a^2 - b^2]))^(\[Beta] \[Nu]) (a + b Cos[c z])^(\[Beta] \[Nu])))/(2 (d - c \[Beta] \[Nu]) (d + c \[Beta] \[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