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Cos




Mathematica Notation

Traditional Notation









Elementary Functions > Cos[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving rational functions > Involving (a z2+b z+c)-n





http://functions.wolfram.com/01.07.21.0161.01









  


  








Input Form





Integrate[(z Cos[d z])/(a z^2 + b z + c), z] == (1/(2 a Sqrt[b^2 - 4 a c])) ((-b + Sqrt[b^2 - 4 a c]) (Cos[((b - Sqrt[b^2 - 4 a c]) d)/(2 a)] CosIntegral[ (d (b - Sqrt[b^2 - 4 a c] + 2 a z))/(2 a)] + Sin[((b - Sqrt[b^2 - 4 a c]) d)/(2 a)] SinIntegral[ (d (b - Sqrt[b^2 - 4 a c] + 2 a z))/(2 a)]) + (b + Sqrt[b^2 - 4 a c]) (Cos[((b + Sqrt[b^2 - 4 a c]) d)/(2 a)] CosIntegral[(d (b + Sqrt[b^2 - 4 a c] + 2 a z))/(2 a)] + Sin[((b + Sqrt[b^2 - 4 a c]) d)/(2 a)] SinIntegral[ (d (b + Sqrt[b^2 - 4 a c] + 2 a z))/(2 a)]))








Standard Form





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MathML Form







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</apply> <ci> d </ci> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> SinIntegral </ci> <apply> <times /> <ci> d </ci> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> <ci> z </ci> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <ci> a </ci> <ci> c </ci> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <cn type='integer'> -1 </cn> </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