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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 functions > Involving cos > Involving cos(b zr+d z+e) sinh(c zr+f z+g)





http://functions.wolfram.com/01.19.21.0766.01









  


  










Input Form





Integrate[Cos[a z^2 + p z + q] Sinh[c z^2 + f z + g], z] == ((-1)^(1/4) E^(g - (I (f - I p)^2)/(4 (a + I c)) - I q) Sqrt[Pi] Erfi[((-1)^(1/4) (f - I p - 2 I a z + 2 c z))/(2 Sqrt[a + c I])])/ (8 Sqrt[a + c I]) - ((I (-1)^(1/4) Sqrt[Pi]) E^(-g + (I (f - I p)^2)/(4 (a + I c)) + I q) Erfi[((-1)^(3/4) (-f + I p - 2 c z + 2 a I z))/(2 Sqrt[a + c I])])/ (8 Sqrt[a + c I]) + ((-1)^(3/4) E^(g + (I (f + I p)^2)/(4 (a - I c)) + I q) Sqrt[Pi] Erfi[((-1)^(3/4) (f + I p + 2 c z + 2 a I z))/(2 Sqrt[a - I c])])/ (8 Sqrt[a - I c]) + ((I (-1)^(3/4) Sqrt[Pi]) E^(-g - (I (f + I p)^2)/(4 (a - I c)) - I q) Erfi[((-1)^(1/4) (-f - I p - 2 I a z - 2 c z))/(2 Sqrt[a - I c])])/ (8 Sqrt[a - I c])










Standard Form





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MathML Form







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</apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 4 </cn> </apply> <apply> <power /> <exponentiale /> <apply> <plus /> <ci> g </ci> <apply> <times /> <imaginaryi /> <apply> <power /> <apply> <plus /> <ci> f </ci> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <imaginaryi /> <ci> q </ci> </apply> </apply> </apply> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> Erfi </ci> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 4 </cn> </apply> <apply> <plus /> <ci> f </ci> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> 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Erfi </ci> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> f </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> 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Rule Form





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





2002-12-18