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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 rational functions of sin > Involving sin(e z) sinh(c z)/a+b sin(d z)





http://functions.wolfram.com/01.19.21.0686.01









  


  










Input Form





Integrate[(Sin[e z] Sinh[c z])/(a + b Sin[d z]), z] == I b ((-(E^((-c + I d + I e) z) Hypergeometric2F1[(d + I (c - I e))/d, 1, (2 d + I (c - I e))/d, (b E^(I d z))/((-I) a + Sqrt[-a^2 + b^2])])/ (((-I) a + Sqrt[-a^2 + b^2]) (d + I (c - I e))) - (E^((-c + I d + I e) z) Hypergeometric2F1[(d + I (c - I e))/d, 1, (2 d + I (c - I e))/d, -((b E^(I d z))/(I a + Sqrt[-a^2 + b^2]))])/ ((I a + Sqrt[-a^2 + b^2]) (d + I (c - I e))) + (E^((c + I d + I e) z) Hypergeometric2F1[(d - I (c + I e))/d, 1, (2 d - I (c + I e))/d, (b E^(I d z))/((-I) a + Sqrt[-a^2 + b^2])])/ (((-I) a + Sqrt[-a^2 + b^2]) (d - I (c + I e))) + (E^((c + I d + I e) z) Hypergeometric2F1[(d - I (c + I e))/d, 1, (2 d - I (c + I e))/d, -((b E^(I d z))/(I a + Sqrt[-a^2 + b^2]))])/ ((I a + Sqrt[-a^2 + b^2]) (d - I (c + I e))) + (E^((-c + I d - I e) z) Hypergeometric2F1[(d + I (c + I e))/d, 1, (2 d + I (c + I e))/d, (b E^(I d z))/((-I) a + Sqrt[-a^2 + b^2])])/ (((-I) a + Sqrt[-a^2 + b^2]) (d + I (c + I e))) + (E^((-c + I d - I e) z) Hypergeometric2F1[(d + I (c + I e))/d, 1, (2 d + I (c + I e))/d, -((b E^(I d z))/(I a + Sqrt[-a^2 + b^2]))])/ ((I a + Sqrt[-a^2 + b^2]) (d + I (c + I e))) - (E^((c + I d - I e) z) Hypergeometric2F1[((-I) c + d - e)/d, 1, ((-I) c + 2 d - e)/d, (b E^(I d z))/((-I) a + Sqrt[-a^2 + b^2])])/ (((-I) a + Sqrt[-a^2 + b^2]) ((-I) c + d - e)) - (E^((c + I d - I e) z) Hypergeometric2F1[((-I) c + d - e)/d, 1, ((-I) c + 2 d - e)/d, -((b E^(I d z))/(I a + Sqrt[-a^2 + b^2]))])/ ((I a + Sqrt[-a^2 + b^2]) ((-I) c + d - e)))/(4 Sqrt[-a^2 + b^2]))










Standard Form





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MathML Form







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<times /> <imaginaryi /> <ci> e </ci> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <apply> <plus /> <ci> d </ci> <apply> <times /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> e </ci> </apply> </apply> </apply> <imaginaryi /> </apply> </apply> <apply> <power /> <ci> d </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> d </ci> </apply> <apply> <times /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> e </ci> </apply> </apply> </apply> <imaginaryi /> </apply> </apply> <apply> <power /> <ci> d </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <apply> <power /> <exponentiale /> <apply> <times /> 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Rule Form





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





2002-12-18