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Sin






Mathematica Notation

Traditional Notation









Elementary Functions > Sin[z] > Integration > Indefinite integration > Involving functions of the direct function, exponential and algebraic functions > Involving powers of the direct function, exponential and algebraic functions > Involving powers of sin, exp and algebraic functions > Involving (a z+b)beta dz sinv(c z+e)





http://functions.wolfram.com/01.06.21.1605.01









  


  










Input Form





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










Standard Form





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MathML Form







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</ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> ExpIntegralE </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#946; </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <ci> b </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> <apply> <ln /> <ci> d </ci> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <ci> Binomial </ci> <ci> v </ci> <apply> <times /> <ci> v </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> v </ci> <ci> &#8469; </ci> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2002-12-18