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Cos






Mathematica Notation

Traditional Notation









Elementary Functions > Cos[z] > Integration > Indefinite integration > Involving functions of the direct function, trigonometric and exponential functions > Involving powers of the direct function, trigonometric and exponential functions > Involving powers of sin and exp > Involving ep zsinmu(c z+d)cosnu(a z)





http://functions.wolfram.com/01.07.21.2615.01









  


  










Input Form





Integrate[E^(p z) Sin[d + c z]^m Cos[a z]^\[Nu], z] == (-((1/(p - I a \[Nu])) ((E^(p z) Binomial[m, m/2] Cos[a z]^\[Nu] Hypergeometric2F1[-((I (p - I a \[Nu]))/(2 a)), -\[Nu], (1/2) (2 - (I p)/a - \[Nu]), -E^(2 I a z)] (-1 + Mod[m, 2]))/ (1 + E^(2 I a z))^\[Nu])) + (Cos[a z]^\[Nu] Sum[(-1)^k E^(I d (-2 k + m)) Binomial[m, k] ((E^(I (4 d k - 2 d m + m Pi + 2 c k z - c m z - I p z)) Hypergeometric2F1[(I (2 I c k - I c m + p + I a \[Nu]))/(2 a), -\[Nu], (I (2 I c k - I c m + p + I a (-2 + \[Nu])))/(2 a), -E^(-2 I a z)])/(I c (2 k - m) + p + I a \[Nu]) + (E^((I c (-2 k + m) + p) z) Hypergeometric2F1[ (I (I c (-2 k + m) + p + I a \[Nu]))/(2 a), -\[Nu], (I (-2 I c k + I c m + p + I a (-2 + \[Nu])))/(2 a), -E^(-2 I a z)])/(I c (-2 k + m) + p + I a \[Nu])), {k, 0, Floor[(1/2) (-1 + m)]}])/(I^m (1 + E^(-2 I a z))^\[Nu]))/2^m /; Element[m, Integers] && m > 0










Standard Form





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MathML Form







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</ci> </apply> <apply> <times /> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <ci> c </ci> <imaginaryi /> <ci> k </ci> </apply> <apply> <times /> <imaginaryi /> <ci> c </ci> <ci> m </ci> </apply> <ci> p </ci> <apply> <times /> <ci> a </ci> <imaginaryi /> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -2 </cn> <imaginaryi /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> c </ci> <imaginaryi /> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> <ci> p </ci> <apply> <times /> <imaginaryi /> <ci> a </ci> <ci> &#957; 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Rule Form





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





2002-12-18