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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 ep z sinm(b z)cos(c zr)





http://functions.wolfram.com/01.07.21.0943.01









  


  










Input Form





Integrate[E^(p z) Sin[b z]^m Cos[c z^2], z] == (1/c) (I 2^(-2 - m) Sqrt[Pi] Binomial[m, m/2] ((Sqrt[(-I) c] Erfi[(p - 2 I c z)/(2 Sqrt[(-I) c])])/E^((I p^2)/(4 c)) - Sqrt[I c] E^((I p^2)/(4 c)) Erfi[(p + 2 I c z)/(2 Sqrt[I c])]) (1 - Mod[m, 2])) + (1/c) (I 2^(-2 - m) Sqrt[Pi] Sum[(-1)^k Binomial[m, k] ((Sqrt[(-I) c] Erfi[((-I) b (2 k - m) + p - 2 I c z)/ (2 Sqrt[(-I) c])])/E^((I (((-I) b (2 k - m) + p)^2 + 2 c m Pi))/ (4 c)) + (Sqrt[(-I) c] Erfi[((-I) b (-2 k + m) + p - 2 I c z)/ (2 Sqrt[(-I) c])])/E^((I (((-I) b (-2 k + m) + p)^2 - 2 c m Pi))/ (4 c)) - Sqrt[I c] E^((I ((I b (2 k - m) + p)^2 + 2 c m Pi))/ (4 c)) Erfi[(I b (2 k - m) + p + 2 I c z)/(2 Sqrt[I c])] - Sqrt[I c] E^((I ((I b (-2 k + m) + p)^2 - 2 c m Pi))/(4 c)) Erfi[(I b (-2 k + m) + p + 2 I c z)/(2 Sqrt[I c])]), {k, 0, Floor[(1/2) (-1 + m)]}]) /; Element[m, Integers] && m > 0










Standard Form





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MathML Form







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Date Added to functions.wolfram.com (modification date)





2002-12-18