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





http://functions.wolfram.com/01.19.21.0600.01









  


  










Input Form





Integrate[Sin[b Sqrt[z] + d z + e] Sinh[c Sqrt[z] + f z + g], z] == (-(1/8)) I (Sqrt[Pi] ((I (b + I c) E^((-I) e - (I (b + I c)^2)/(4 (d + I f)) - g) (E^(2 I e) Erf[(b + I c + 2 (d + I f) Sqrt[z])/(2 Sqrt[I d - f])] + E^((I (b + I c)^2)/(2 (d + I f)) + 2 g) Erfi[(b + I c + 2 (d + I f) Sqrt[z])/(2 Sqrt[I d - f])]))/ (Sqrt[I d - f] (d + I f)) + (1/(I d + f)^(3/2)) ((I b + c) ((-E^((-I) e + (I b + c)^2/(4 (I d + f)) - g)) Erf[(I b + c + 2 (I d + f) Sqrt[z])/(2 Sqrt[I d + f])] - E^(I e - (I b + c)^2/(4 (I d + f)) + g) Erfi[(I b + c + 2 (I d + f) Sqrt[z])/(2 Sqrt[I d + f])]))) - (4 Sin[e + I g + b Sqrt[z] + I c Sqrt[z] + d z + I f z])/(d + I f) + (4 Sin[e - I g + b Sqrt[z] - I c Sqrt[z] + d z - I f z])/(d - I f))










Standard Form





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MathML Form







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<apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> c </ci> </apply> <apply> <times /> <ci> f </ci> <ci> z </ci> </apply> <ci> g </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 8 </cn> </apply> <imaginaryi /> <apply> <plus /> <apply> <times /> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> d </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> f </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <ci> d </ci> <apply> <times /> <imaginaryi /> <ci> f </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <imaginaryi /> <apply> <plus /> <ci> b </ci> <apply> <times 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Rule Form





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





2002-12-18