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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/01.07.21.0952.01









  


  










Input Form





Integrate[E^(b z^r + e) Sin[a z^r + q]^m Cos[c z^r + g], z] == (-(1/r)) 2^(-1 - m) z (E^(e - I g) Binomial[m, m/2] (Gamma[1/r, (-(b - I c)) z^r]/((-(b - I c)) z^r)^r^(-1) + (E^(2 I g) Gamma[1/r, (-(b + I c)) z^r])/((-(b + I c)) z^r)^r^(-1)) (1 - Mod[m, 2]) + Sum[((-1)^k Binomial[m, k] ((E^(2 I m q) Gamma[1/r, (-(b - I (c + 2 a k - a m))) z^r])/ ((-(b - I (c + 2 a k - a m))) z^r)^r^(-1) + (E^(I (2 g + m Pi + 4 k q)) Gamma[1/r, (-(b + I (c + 2 a k - a m))) z^r])/((-(b + I (c + 2 a k - a m))) z^r)^r^(-1) + (E^(I (m Pi + 4 k q)) Gamma[1/r, (-(b - I (c - 2 a k + a m))) z^r])/ ((-(b - I (c - 2 a k + a m))) z^r)^r^(-1) + (E^(2 I (g + m q)) Gamma[1/r, (-(b + I (c - 2 a k + a m))) z^r])/ ((-(b + I (c - 2 a k + a m))) z^r)^r^(-1)))/ E^((1/2) I (2 I e + 2 g + m Pi + 4 k q + 2 m q)), {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