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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(b zr+e) cos(c zr+g)





http://functions.wolfram.com/01.07.21.0706.01









  


  










Input Form





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