Cosine: Integration (formula 01.07.21.0664)

Cos

$Mathematica Notation$

Elementary Functions

Cos[z]

Integration

Indefinite integration

Involving one direct function and elementary functions

Involving trigonometric functions

Involving powers of sin

Involving sin^mu(c z+d)cos(a z)

http://functions.wolfram.com/01.07.21.0664.01

Input Form

Integrate[Sin[d + c z]^\[Mu] Cos[a z], z] == (-(1/(2 (a^2 - c^2 \[Mu]^2)))) ((I (E^(2 I a z) (a + c \[Mu]) Hypergeometric2F1[(a - c \[Mu])/(2 c), -\[Mu], (1/2) (2 + a/c - \[Mu]), E^(2 I (d + c z))] + (-a + c \[Mu]) Hypergeometric2F1[-((a + c \[Mu])/(2 c)), -\[Mu], -((a + c (-2 + \[Mu]))/(2 c)), E^(2 I (d + c z))]) Sin[d + c z]^\[Mu])/ (E^(I a z) (1 - E^(2 I (d + c z)))^\[Mu]))

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