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Sin






Mathematica Notation

Traditional Notation









Elementary Functions > Sin[z] > Integration > Indefinite integration > Involving functions of the direct function, exponential and a power functions > Involving powers of the direct function, exponential and a power functions > Involving powers of sin, exp and power > Involving zalpha-1 ep z sinnu(a z+b)





http://functions.wolfram.com/01.06.21.1465.01









  


  










Input Form





Integrate[z^n E^(p z) Sin[a z + b]^v, z] == (-2^(-v)) z^(1 + n) Binomial[v, v/2] ExpIntegralE[-n, (-p) z] (1 - Mod[v, 2]) - (z^(1 + n) Sum[((-1)^s Binomial[v, s] (E^(2 I b v) ExpIntegralE[-n, (-p - I a (-2 s + v)) z] + E^(I (4 b s + Pi v)) ExpIntegralE[-n, (-p + I a (-2 s + v)) z]))/ E^((1/2) I (Pi v + 2 b (2 s + v))), {s, 0, Floor[(1/2) (-1 + v)]}])/ 2^v /; Element[n, Integers] && Element[v, Integers] && v >= 0










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