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Sec






Mathematica Notation

Traditional Notation









Elementary Functions > Sec[z] > Integration > Indefinite integration > Involving functions of the direct function > Involving algebraic functions of the direct function > Involving (a+b sec2(c z))beta





http://functions.wolfram.com/01.11.21.0096.01









  


  










Input Form





Integrate[(a + b Sec[c z]^2)^\[Beta], z] == (1/(-c + 2 c \[Beta])) ((AppellF1[1/2 - \[Beta], 1/2, -\[Beta], 3/2 - \[Beta], Cos[c z]^2, -((a Cos[c z]^2)/b)] Cot[c z] (a + b Sec[c z]^2)^\[Beta] Sqrt[Sin[c z]^2])/(1 + (a Cos[c z]^2)/b)^\[Beta])










Standard Form





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MathML Form







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</mi> </msup> <mo> &#8290; </mo> <msqrt> <mrow> <msup> <mi> sin </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </msqrt> </mrow> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> <mo> &#8290; </mo> <mi> &#946; </mi> </mrow> <mo> - </mo> <mi> c </mi> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <semantics> <msub> <mi> F </mi> <mn> 1 </mn> </msub> <annotation-xml encoding='MathML-Content'> <ci> AppellF1 </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> - </mo> <mi> &#946; </mi> </mrow> <mo> ; </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mrow> <mrow> <mo> - </mo> <mi> &#946; </mi> </mrow> <mo> ; </mo> <mrow> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> <mo> - </mo> <mi> &#946; </mi> </mrow> <mo> ; </mo> <mrow> <msup> <mi> cos </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> a </mi> <mo> &#8290; 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Rule Form





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





2002-10-15





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