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Sin




Mathematica Notation

Traditional 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 zalpha-1 sinnu(a z+b)





http://functions.wolfram.com/01.06.21.1038.01









  


  








Input Form





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