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Sinh






Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Integration > Indefinite integration > Involving functions of the direct function > Involving products of powers of the direct function > Involving product of power of the direct function and the direct function > Involving sinh(c z)sinhnu(a z)





http://functions.wolfram.com/01.19.21.1535.01









  


  










Input Form





Integrate[Sinh[c z] Sinh[a z]^v, z] == (E^((I Pi v)/2) Binomial[v, v/2] Cosh[c z] (1 - Mod[v, 2]))/(2^v c) + 2^(-1 - v) Sum[(-1)^k (E^((c - 2 a k + a v) z)/(c - 2 a k + a v) + E^(I Pi v + (-c + 2 a k - a v) z)/(c - (2 a k - a v)) + E^((-c - 2 a k + a v) z)/(c + (2 a k - a v)) + E^(I Pi v + (c + 2 a k - a v) z)/(c + (2 a k - a v))) Binomial[v, k], {k, 0, Floor[(1/2) (-1 + v)]}] /; Element[v, Integers] && v > 0










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