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Cos




Mathematica Notation

Traditional Notation









Elementary Functions > Cos[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving exponential function and a power function > Involving exp and power > Involving zalpha-1eb zrcos(c zr+g)





http://functions.wolfram.com/01.07.21.0422.01









  


  








Input Form





Integrate[z^n E^(b Sqrt[z]) Cos[c Sqrt[z] + g], z] == ((-E^(I g)) (-(ExpIntegralEi[(-(-b - I c)) Sqrt[z]]/(-2 (1 + n))!) + Sum[((-b - I c) Sqrt[z])^k/Pochhammer[2 (1 + n), -1 + k - 2 n], {k, 0, 2 n + 1}]/E^((-b - I c) Sqrt[z]) - Sum[((-b - I c) Sqrt[z])^k/Pochhammer[2 (1 + n), -1 + k - 2 n], {k, 2 (1 + n), -1}]/E^((-b - I c) Sqrt[z])))/(b + I c)^(2 (1 + n)) - (-(ExpIntegralEi[(-(-b + I c)) Sqrt[z]]/(-2 (1 + n))!) + Sum[((-b + I c) Sqrt[z])^k/Pochhammer[2 (1 + n), -1 + k - 2 n], {k, 0, 2 n + 1}]/E^((-b + I c) Sqrt[z]) - Sum[((-b + I c) Sqrt[z])^k/Pochhammer[2 (1 + n), -1 + k - 2 n], {k, 2 (1 + n), -1}]/E^((-b + I c) Sqrt[z]))/ (E^(I g) (-b + I c)^(2 (1 + n))) /; Element[n, Integers]








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