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Sinh






Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving trigonometric and exponential functions > Involving products of sin and exp > Involving ep z sin(a z) sin(b z) sinh(c z)





http://functions.wolfram.com/01.19.21.1240.01









  


  










Input Form





Integrate[E^(p z) Sin[a z] Sin[b z] Sinh[c z], z] == (-(1/4)) E^(p z) ((((-I) a + I b + c) Cos[(a - b + I c) z] + I p Sin[(a - b + I c) z])/((a - b + I (c - p)) (a - b + I (c + p))) + (I ((a + b + I c) Cos[(a + b + I c) z] - p Sin[(a + b + I c) z]))/ ((a + b + I (c - p)) (a + b + I (c + p))) + ((I a - I b + c) Cosh[(I a - I b + c) z] - p Sinh[(I a - I b + c) z])/ (a^2 + b^2 - 2 a (b + I c) + 2 I b c - c^2 + p^2) + ((-I) (a + b - I c) Cosh[(I a + I b + c) z] + p Sinh[(I a + I b + c) z])/ ((a + b - I (c - p)) (a + b - I (c + p))))










Standard Form





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MathML Form







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<ci> a </ci> <ci> b </ci> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> </apply> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> p </ci> <apply> <sin /> <apply> <times /> <apply> <plus /> <ci> a </ci> <ci> b </ci> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> </apply> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> a </ci> <ci> b </ci> <apply> <times /> <imaginaryi /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> p </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <ci> a </ci> <ci> b </ci> <apply> <times /> <imaginaryi /> <apply> <plus /> <ci> c </ci> <ci> p </ci> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <ci> p </ci> <apply> <sinh /> <apply> <times /> <apply> <plus /> <ci> c </ci> <apply> <times /> 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-1 </cn> <apply> <times /> <imaginaryi /> <apply> <plus /> <ci> c </ci> <ci> p </ci> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> b </ci> </apply> </apply> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> <apply> <cosh /> <apply> <times /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> b </ci> </apply> </apply> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> p </ci> <apply> <sinh /> <apply> <times /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> b </ci> </apply> </apply> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> b </ci> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> </apply> <ci> a </ci> </apply> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <ci> p </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> b </ci> <ci> c </ci> </apply> </apply> <cn type='integer'> -1 </cn> </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