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Sin






Mathematica Notation

Traditional Notation









Elementary Functions > Sin[z] > Integration > Indefinite integration > Involving functions of the direct function > Involving products of powers of the direct function > Involving product of power of the direct function and the direct function > Involving sin(c z+d)sinv(a z)





http://functions.wolfram.com/01.06.21.0703.01









  


  










Input Form





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










Standard Form





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MathML Form







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</apply> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> <ci> k </ci> </apply> </apply> <apply> <times /> <ci> a </ci> <ci> v </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> Binomial </ci> <ci> v </ci> <ci> k </ci> </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