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Cos






Mathematica Notation

Traditional Notation









Elementary Functions > Cos[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving trigonometric functions > Involving powers of sin > Involving sinm(d z) cos(c zr+f z)





http://functions.wolfram.com/01.07.21.0713.01









  


  










Input Form





Integrate[Sin[d z]^m Cos[c z^2 + f z], z] == (1/Sqrt[c]) (2^(-(1/2) - m) Sqrt[Pi] Binomial[m, m/2] (1 - Mod[m, 2]) (Cos[f^2/(4 c)] FresnelC[(f + 2 c z)/(Sqrt[c] Sqrt[2 Pi])] + FresnelS[(f + 2 c z)/(Sqrt[c] Sqrt[2 Pi])] Sin[f^2/(4 c)])) + 2^(-(1/2) - m) Sqrt[Pi] Sum[(-1)^k Binomial[m, k] ((1/Sqrt[-c]) (Cos[(-f + 2 d k - d m)^2/(4 c) + (m Pi)/2] FresnelC[(-f + 2 d k - d m - 2 c z)/(Sqrt[-c] Sqrt[2 Pi])] - FresnelS[(-f + 2 d k - d m - 2 c z)/(Sqrt[-c] Sqrt[2 Pi])] Sin[(-f + 2 d k - d m)^2/(4 c) + (m Pi)/2]) + (1/Sqrt[c]) (Cos[-((f + 2 d k - d m)^2/(4 c)) + (m Pi)/2] FresnelC[(f + 2 d k - d m + 2 c z)/(Sqrt[c] Sqrt[2 Pi])] - FresnelS[(f + 2 d k - d m + 2 c z)/(Sqrt[c] Sqrt[2 Pi])] Sin[-((f + 2 d k - d m)^2/(4 c)) + (m Pi)/2])), {k, 0, Floor[(1/2) (-1 + m)]}] /; Element[m, Integers] && m > 0










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