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Sin






Mathematica Notation

Traditional Notation









Elementary Functions > Sin[z] > Integration > Indefinite integration > Involving functions of the direct function and exponential function > Involving powers of the direct function and exponential function > Involving powers of sin and exp > Involving eb zr+d z+e sinv(c zr+f z+g)





http://functions.wolfram.com/01.06.21.1341.01









  


  










Input Form





Integrate[E^(b z^2 + d z + e) Sin[c z^2 + f z + g]^v, z] == (2^(-1 - v) E^(-(d^2/(4 b)) + e) Sqrt[Pi] Binomial[v, v/2] Erfi[(d + 2 b z)/(2 Sqrt[b])] (1 - Mod[v, 2]))/Sqrt[b] + (2^(-1 - v) Sqrt[Pi] Sum[(-1)^k Binomial[v, k] (-((E^((1/4) (4 e + 8 I g k - 4 I g v + 4 I Pi v - (d + 2 I f k - I f v)^2/(b + 2 I c k - I c v))) Erf[(d + 2 I f k - I f v + 2 b z + 4 I c k z - 2 I c v z)/ (2 Sqrt[-b - 2 I c k + I c v])])/Sqrt[-b - 2 I c k + I c v]) + (E^(e + I g (-2 k + v) - (d + I f (-2 k + v))^2/ (4 (b + I c (-2 k + v)))) Erfi[(d - 2 I f k + I f v + 2 b z - 4 I c k z + 2 I c v z)/(2 Sqrt[b - 2 I c k + I c v])])/ Sqrt[b - 2 I c k + I c 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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</apply> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <floor /> <apply> <times /> <apply> <plus /> <ci> v </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </uplimit> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <apply> <ci> Binomial </ci> <ci> v </ci> <ci> k </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> d </ci> <apply> <times /> <ci> f </ci> <imaginaryi /> <apply> <plus /> <ci> v </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <ci> b </ci> <apply> <times /> <ci> c </ci> <imaginaryi /> <apply> <plus /> <ci> v </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <ci> e </ci> <apply> <times /> <ci> g </ci> <imaginaryi /> <apply> <plus /> <ci> v </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <ci> Erfi </ci> <apply> <times /> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> f </ci> <ci> k </ci> </apply> </apply> <apply> <times /> <imaginaryi /> <ci> f </ci> <ci> v </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b 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<imaginaryi /> <ci> c </ci> <ci> v </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> f </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> f </ci> <ci> v </ci> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> c </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> c </ci> <ci> v </ci> </apply> </apply> 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Rule Form





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





2002-12-18