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Sin






Mathematica Notation

Traditional Notation









Elementary Functions > Sin[z] > Integration > Indefinite integration > Involving functions of the direct function and exponential function > Involving powers of the direct function and exponential function > Involving powers of sin and exp > Involving eb zr+esinv(c zr+g)





http://functions.wolfram.com/01.06.21.1314.01









  


  










Input Form





Integrate[E^(b Sqrt[z] + e) Sin[c Sqrt[z] + g]^v, z] == 2^(1 - v) Binomial[v, v/2] (1 - Mod[v, 2]) ((E^(e + b Sqrt[z]) (-1 + b Sqrt[z]))/b^2) + 2^(2 - v) E^(e + b Sqrt[z]) Sum[(-1)^k Binomial[v, k] (((-b^2 + c^2 (2 k - v)^2 + b^3 Sqrt[z] + b c^2 (2 k - v)^2 Sqrt[z]) Cos[(Pi v)/2 - g (-2 k + v) + c (2 k - v) Sqrt[z]] + c (2 k - v) (-2 b + b^2 Sqrt[z] + c^2 (2 k - v)^2 Sqrt[z]) Sin[(Pi v)/2 - g (-2 k + v) + c (2 k - v) Sqrt[z]])/(b^2 + c^2 (2 k - v)^2)^2), {k, 0, Floor[(1/2) (-1 + v)]}] /; Element[v, Integers] && v > 0










Standard Form





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MathML Form







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<cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> g </ci> <apply> <plus /> <ci> v </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> v </ci> <apply> <ci> SuperPlus </ci> <ci> &#8469; </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2002-12-18