Cosine: Integration (formula 01.07.21.1387)

Cos

$Mathematica Notation$

Elementary Functions

Cos[z]

Integration

Indefinite integration

Involving functions of the direct function

Involving algebraic functions of the direct function

Involving ((a+b cos²(c z))^nu)^betacos(d z)

http://functions.wolfram.com/01.07.21.1387.01

Input Form

Integrate[((a + b Cos[c z]^2)^\[Nu])^\[Beta] Cos[c z], z] == -((a + b Cos[c z]^2) ((a + b Cos[c z]^2)^\[Nu])^\[Beta] Csc[c z] Hypergeometric2F1[1 + \[Beta] \[Nu], 1/2, 2 + \[Beta] \[Nu], (a + b Cos[c z]^2)/(a + b)] Sqrt[(b Sin[c z]^2)/(a + b)])/ (2 b c (1 + \[Beta] \[Nu]))

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