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Cos




Mathematica Notation

Traditional Notation









Elementary Functions > Cos[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving trigonometric and a power functions > Involving sin and power > Involving zalpha-1sin(c z)cos(a z+b)





http://functions.wolfram.com/01.07.21.0754.01









  


  








Input Form





Integrate[z^(\[Alpha] - 1) Sin[c z] Cos[b + a z], z] == ((1/4) I z^\[Alpha] (((a - c)^2 z^2)^\[Alpha] ((-((-I) (a + c) z)^\[Alpha]) Gamma[\[Alpha], I (a + c) z] (Cos[b] - I Sin[b]) + (I (a + c) z)^\[Alpha] Gamma[\[Alpha], (-I) (a + c) z] (Cos[b] + I Sin[b])) - (I (a - c) z)^\[Alpha] ((a + c)^2 z^2)^\[Alpha] Gamma[\[Alpha], (-I) (a - c) z] (Cos[b] + I Sin[b]) + ((-I) (a - c) z)^\[Alpha] ((a + c)^2 z^2)^\[Alpha] Gamma[\[Alpha], I (a - c) z] (Cos[b] - I Sin[b])))/ (((a - c)^2 z^2)^\[Alpha] ((a + c)^2 z^2)^\[Alpha])








Standard Form





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MathML Form







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</ci> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> a </ci> <ci> c </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <ci> &#945; </ci> </apply> <apply> <ci> Gamma </ci> <ci> &#945; </ci> <apply> <times /> <imaginaryi /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <cos /> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <sin /> <ci> b </ci> </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