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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 products of powers of the direct function, exponential and a power functions > Involving product of power of the direct function, the direct function, exponential and a power functions > Involving zalpha-1ep zsin(c z) sinv(a z+b)





http://functions.wolfram.com/01.06.21.1565.01









  


  










Input Form





Integrate[z^(\[Alpha] - 1) E^(p z) Sin[c z] Sin[b + a z]^v, z] == (-2^(-1 - v)) I z^\[Alpha] (Binomial[v, v/2] ((-(((-I) c - p) z)^(-\[Alpha])) Gamma[\[Alpha], (-I) c z - p z] + Gamma[\[Alpha], I c z - p z]/ (I (c + I p) z)^\[Alpha]) (1 - Mod[v, 2]) + Sum[((-1)^k Binomial[v, k] (((-E^(I (4 b k + Pi v))) Gamma[\[Alpha], (-I) (c + 2 a k - I p - a v) z])/((-I) (c + 2 a k - I p - a v) z)^ \[Alpha] + (E^(2 I b v) Gamma[\[Alpha], I (c + 2 a k + I p - a v) z])/(I (c + 2 a k + I p - a v) z)^\[Alpha] - (E^(2 I b v) Gamma[\[Alpha], (-I) (c - 2 a k - I p + a v) z])/ ((-I) (c - 2 a k - I p + a v) z)^\[Alpha] + (E^(I (4 b k + Pi v)) Gamma[\[Alpha], I (c - 2 a k + I p + a v) z])/ (I (c - 2 a k + I p + a v) z)^\[Alpha]))/E^(I b (2 k + v)), {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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Rule Form





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





2002-12-18