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Sin






Mathematica Notation

Traditional Notation









Elementary Functions > Sin[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Arguments involving polynomials or algebraic functions and factors involving exponential functions > Involving exp > Involving ab zr+d z sin(c zr+f z+g)





http://functions.wolfram.com/01.06.21.0585.01









  


  










Input Form





Integrate[a^(b z^2 + d z) Sin[c z^2 + f z + g], z] == (I a^((d f)/(-2 c + 2 I b Log[a]) + (b (f^2 - d^2 Log[a]^2))/ (2 (c^2 + b^2 Log[a]^2))) Sqrt[Pi] (a^((I b d f Log[a])/(c^2 + b^2 Log[a]^2)) E^((-f^2 + d^2 Log[a]^2)/(4 I c + 4 b Log[a]) - I g) Erfi[((-I) (f + 2 c z) + (d + 2 b z) Log[a])/ (2 Sqrt[(-I) c + b Log[a]])] Sqrt[(-I) c + b Log[a]] (I c + b Log[a]) + E^((-f^2 + d^2 Log[a]^2)/(-4 I c + 4 b Log[a]) + I g) Erfi[(I (f + 2 c z) + (d + 2 b z) Log[a])/(2 Sqrt[I c + b Log[a]])] (I c - b Log[a]) Sqrt[I c + b Log[a]]))/(4 (c^2 + b^2 Log[a]^2))










Standard Form





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MathML Form







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<power /> <exponentiale /> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> d </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <ln /> <ci> a </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> f </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <imaginaryi /> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <ci> b </ci> <apply> <ln /> <ci> a </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> g </ci> </apply> </apply> </apply> </apply> <apply> <ci> Erfi </ci> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> z </ci> </apply> </apply> <apply> <ln /> <ci> a </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <plus /> <ci> f </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <ci> c </ci> </apply> <apply> <times /> <ci> b </ci> <apply> <ln /> <ci> a </ci> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <ci> c </ci> </apply> <apply> <times /> <ci> b </ci> <apply> <ln /> <ci> a </ci> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> <apply> <times /> <ci> b </ci> <apply> <ln /> <ci> a </ci> </apply> </apply> </apply> <apply> <power /> <ci> a </ci> <apply> <times /> <imaginaryi /> <ci> b </ci> <ci> d </ci> <ci> f </ci> <apply> <ln /> <ci> a </ci> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <ln /> <ci> a </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> d </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <ln /> <ci> a </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> f </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> -4 </cn> <imaginaryi /> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <ci> b </ci> <apply> <ln /> <ci> a </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <imaginaryi /> <ci> g </ci> </apply> </apply> </apply> <apply> <ci> Erfi </ci> <apply> <times /> <apply> <plus /> <apply> <times /> <imaginaryi /> <apply> <plus /> <ci> f </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> z </ci> </apply> </apply> <apply> <ln /> <ci> a </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> <apply> <times /> <ci> b </ci> <apply> <ln /> <ci> a </ci> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> <apply> <times /> <ci> b </ci> <apply> <ln /> <ci> a </ci> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <apply> <ln /> <ci> a </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2002-12-18