Cosine: Integration (formula 01.07.21.2391)

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 sin²(e z)+b cos²(e z))^beta

http://functions.wolfram.com/01.07.21.2391.01

Input Form

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

Standard Form

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MathML Form

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Rule Form

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

2002-12-18