Cosine: Integration (formula 01.07.21.2407)

Cos

$Mathematica Notation$

Elementary Functions

Cos[z]

Integration

Indefinite integration

Involving functions of the direct function and trigonometric functions

Involving algebraic functions of the direct function and trigonometric functions

Involving algebraic functions of sin

Involving (a +b sin²(e z)+c cos²(e z))^beta

http://functions.wolfram.com/01.07.21.2407.01

Input Form

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

Standard Form

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MathML Form

<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> <msup> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mrow> <mi> b </mi> <mo> ⁢ </mo> <mrow> <msup> <mi> sin </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mi> e </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mrow> <msup> <mi> cos </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mi> e </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mi> β </mi> </msup> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <mn> 1 </mn> <mi> e </mi> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <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> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ; 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Rule Form

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

2002-12-18