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Sin






Mathematica Notation

Traditional Notation









Elementary Functions > Sin[z] > Integration > Indefinite integration > Involving functions of the direct function > Involving algebraic functions of the direct function > Involving ((a+b sin(2c z))m)+-1/2sin(c z)





http://functions.wolfram.com/01.06.21.0917.01









  


  










Input Form





Integrate[Sqrt[(a + b Sin[2 c z])^3] Sin[c z], z] == -(Sqrt[(a + b Sin[2 c z])^3] (3 (a + b)^2 ArcTan[(Sqrt[b] (Cos[c z] - Sin[c z]))/ Sqrt[a + b Sin[2 c z]]] - 6 a b ArcTanh[(Sqrt[b] (Cos[c z] + Sin[c z]))/Sqrt[a + b Sin[2 c z]]] + 3 a^2 Log[Sqrt[b] Cos[c z] + Sqrt[b] Sin[c z] + Sqrt[a + b Sin[2 c z]]] + 3 b^2 Log[Sqrt[b] Cos[c z] + Sqrt[b] Sin[c z] + Sqrt[a + b Sin[2 c z]]] + 10 a Sqrt[b] Cos[c z] Sqrt[a + b Sin[2 c z]] - 4 b^(3/2) Sin[c z] Sqrt[a + b Sin[2 c z]] + 2 b^(3/2) Sqrt[a + b Sin[2 c z]] Sin[3 c z]))/ (16 Sqrt[b] c (a + b Sin[2 c z])^(3/2))










Standard Form





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MathML Form







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<apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> b </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <cos /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <ci> b </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <sin /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <ci> b </ci> <apply> <sin /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 16 </cn> <apply> <power /> <ci> b </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> c </ci> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <ci> b </ci> <apply> <sin /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2002-12-18