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Sinh




Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Integration > Indefinite integration > Involving functions of the direct function, trigonometric and exponential functions > Involving rational functions of the direct function, trigonometric and exponential functions > Involving cos and exp > Involving ep zcos(d z)/a+b sinh2(c z)





http://functions.wolfram.com/01.19.21.3282.01









  


  








Input Form





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








Standard Form





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MathML Form







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<mo> + </mo> <mfrac> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> </mrow> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> d </mi> </mrow> <mo> + </mo> <mi> p </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> </msup> <mo> &#8290; </mo> <semantics> <mrow> <mrow> <msub> <mo> &#8202; </mo> <mn> 2 </mn> </msub> <msub> <mi> F </mi> <mn> 1 </mn> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> </mrow> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> d </mi> </mrow> <mo> + </mo> <mi> p </mi> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> </mrow> </mfrac> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ; </mo> <mfrac> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> c </mi> </mrow> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> d </mi> </mrow> <mo> + </mo> <mi> p </mi> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> </mrow> </mfrac> <mo> ; </mo> <mfrac> <mrow> <mi> b </mi> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </msup> </mrow> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mi> a </mi> </msqrt> </mrow> <mo> + </mo> <mi> b </mi> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox[&quot;\[InvisiblePrefixScriptBase]&quot;, FormBox[&quot;2&quot;, TraditionalForm]], SubscriptBox[&quot;F&quot;, FormBox[&quot;1&quot;, TraditionalForm]]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, 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<apply> <power /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> d </ci> </apply> </apply> <ci> p </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