Sine: Integration (formula 01.06.21.1015)

Sin

$Mathematica Notation$

Elementary Functions

Sin[z]

Integration

Indefinite integration

Involving functions of the direct function and a power function

Involving powers of the direct function and a power function

Involving powers of sin and power

Involving z^alpha-1 sin^v(a z)

http://functions.wolfram.com/01.06.21.1015.01

Input Form

Integrate[z Sin[a z]^v, z] == (1/(2 a^2)) (Sin[a z]^(1 + v) ((2 a z Cos[a z] Hypergeometric2F1[1, (2 + v)/2, (3 + v)/2, Sin[a z]^2])/ (1 + v) - 2^(-1 - v) Sqrt[Pi] Gamma[1 + v] HypergeometricPFQRegularized[ {1, (2 + v)/2, (2 + v)/2}, {(3 + v)/2, (4 + v)/2}, Sin[a z]^2] Sin[a z]))

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