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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+d)cos(a z)





http://functions.wolfram.com/01.07.21.0753.01









  


  










Input Form





Integrate[z^(\[Alpha] - 1) Sin[d + c z] Cos[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[d] - I Sin[d]) + (I (a + c) z)^\[Alpha] Gamma[\[Alpha], (-I) (a + c) z] (Cos[d] + I Sin[d])) - (I (a - c) z)^\[Alpha] ((a + c)^2 z^2)^\[Alpha] Gamma[\[Alpha], (-I) (a - c) z] (Cos[d] - I Sin[d]) + ((-I) (a - c) z)^\[Alpha] ((a + c)^2 z^2)^\[Alpha] Gamma[\[Alpha], I (a - c) z] (Cos[d] + I Sin[d])))/ (((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 /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <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> d </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <sin /> <ci> d </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