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Sin






Mathematica Notation

Traditional Notation









Elementary Functions > Sin[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving exponential function and a power function > Involving exp and power > Involving zn eb z+e sin(c zr)





http://functions.wolfram.com/01.06.21.0377.01









  


  










Input Form





Integrate[z^n E^(b z + e) Sin[c z^2], z] == (-(1/4)) I ((-I) c)^(-1 - n) E^(e - (I b^2)/(4 c)) Sum[2^(k - n) (-b)^(-k + n) (b - 2 I c z)^(1 + k) (-((I (b - 2 I c z)^2)/c))^((1/2) (-1 - k)) Binomial[n, k] Gamma[(1 + k)/2, -((I (b - 2 I c z)^2)/(4 c))], {k, 0, n}] + (1/4) I (I c)^(-1 - n) E^((I b^2)/(4 c) + e) Sum[2^(k - n) (-b)^(-k + n) (b + 2 I c z)^(1 + k) ((I (b + 2 I c z)^2)/c)^((1/2) (-1 - k)) Binomial[n, k] Gamma[(1 + k)/2, (I (b + 2 I c z)^2)/(4 c)], {k, 0, n}] /; Element[n, Integers] && n >= 0










Standard Form





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MathML Form







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Gamma </ci> <apply> <times /> <apply> <plus /> <ci> k </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <power /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> n </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