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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 and exponential functions > Involving powers of sin and exp > Involving eb zr+e sinm(a zr+q) cos(c zr+g)





http://functions.wolfram.com/01.07.21.0953.01









  


  










Input Form





Integrate[E^(b z^2 + e) Sin[a z^2 + q]^m Cos[c z^2 + g], z] == 2^(-2 - m) E^(e - I g) Sqrt[Pi] Binomial[m, m/2] (Erfi[Sqrt[b - I c] z]/Sqrt[b - I c] + (E^(2 I g) Erfi[Sqrt[b + I c] z])/ Sqrt[b + I c]) (1 - Mod[m, 2]) + 2^(-2 - m) Sqrt[Pi] Sum[(-1)^k Binomial[m, k] ((E^(e - I g + (I m Pi)/2 - I (-2 k + m) q) Erfi[Sqrt[b - I c - I a (-2 k + m)] z])/ Sqrt[b - I c - I a (-2 k + m)] + (E^(e + I g + (I m Pi)/2 - I (-2 k + m) q) Erfi[Sqrt[b + I c - I a (-2 k + m)] z])/ Sqrt[b + I c - I a (-2 k + m)] + (E^(e - I g - (I m Pi)/2 + I (-2 k + m) q) Erfi[Sqrt[b - I c + I a (-2 k + m)] z])/ Sqrt[b - I c + I a (-2 k + m)] + (E^(e + I g - (I m Pi)/2 + I (-2 k + m) q) Erfi[Sqrt[b + I c + I a (-2 k + m)] z])/ Sqrt[b + I c + I a (-2 k + m)]), {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