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Cos






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.07.21.2385.01









  


  










Input Form





Integrate[1/Sqrt[a + b Sin[e z] + c Cos[e z]], z] == (1/(b Sqrt[1 + c^2/b^2] e)) (2 AppellF1[1/2, 1/2, 1/2, 3/2, (a + c Cos[e z] + b Sin[e z])/(a + b Sqrt[1 + c^2/b^2]), (a + c Cos[e z] + b Sin[e z])/(a - b Sqrt[1 + c^2/b^2])] Sec[e z + ArcTan[c/b]] Sqrt[((-c) Cos[e z] + b (Sqrt[1 + c^2/b^2] - Sin[e z]))/ (a + b Sqrt[1 + c^2/b^2])] Sqrt[a + c Cos[e z] + b Sin[e z]] Sqrt[(c Cos[e z] + b (Sqrt[1 + c^2/b^2] + Sin[e z]))/ (-a + b Sqrt[1 + c^2/b^2])])










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