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http://functions.wolfram.com/01.06.21.0513.01
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Integrate[Sin[a Tanh[z]], z] == (1/2) ((-CosIntegral[a - a Tanh[z]]) Sin[a] -
CosIntegral[a + a Tanh[z]] Sin[a] +
Cos[a] (SinIntegral[a - a Tanh[z]] + SinIntegral[a + a Tanh[z]]))
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mo> ∫ </mo> <mrow> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mi> tanh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mrow> <mi> Ci </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mrow> <mi> tanh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mrow> <mi> Ci </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mi> tanh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Si </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mrow> <mi> tanh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> Si </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mi> tanh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <sin /> <apply> <times /> <ci> a </ci> <apply> <tanh /> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> CosIntegral </ci> <apply> <plus /> <apply> <times /> <apply> <tanh /> <ci> z </ci> </apply> <ci> a </ci> </apply> <ci> a </ci> </apply> </apply> </apply> <apply> <sin /> <ci> a </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> CosIntegral </ci> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <apply> <tanh /> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> <apply> <sin /> <ci> a </ci> </apply> </apply> </apply> <apply> <times /> <apply> <cos /> <ci> a </ci> </apply> <apply> <plus /> <apply> <ci> SinIntegral </ci> <apply> <plus /> <apply> <times /> <apply> <tanh /> <ci> z </ci> </apply> <ci> a </ci> </apply> <ci> a </ci> </apply> </apply> <apply> <ci> SinIntegral </ci> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <apply> <tanh /> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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Date Added to functions.wolfram.com (modification date)
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