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Sinh






Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving trigonometric and exponential functions > Involving powers of sin and exp > Involving ep zr sinm(b zr)sinh(c zr)





http://functions.wolfram.com/01.19.21.1228.01









  


  










Input Form





Integrate[E^(p z^r) Sin[b z^r]^m Sinh[c z^r], z] == (1/r) 2^(-1 - m) z Binomial[m, m/2] ((-((-c - p) z^r)^(-r^(-1))) Gamma[1/r, (-c - p) z^r] + Gamma[1/r, (c - p) z^r]/ ((c - p) z^r)^r^(-1)) (1 - Mod[m, 2]) + (1/r) 2^(-1 - m) z Sum[(-1)^k Binomial[m, k] (((-E^((-(1/2)) I m Pi)) Gamma[1/r, (-c + 2 I b k - I b m - p) z^r])/ ((-c + 2 I b k - I b m - p) z^r)^r^(-1) + Gamma[1/r, (c + 2 I b k - I b m - p) z^r]/(E^((1/2) I m Pi) ((c + 2 I b k - I b m - p) z^r)^r^(-1)) - (E^((I m Pi)/2) Gamma[1/r, (-c - 2 I b k + I b m - p) z^r])/ ((-c - 2 I b k + I b m - p) z^r)^r^(-1) + (E^((I m Pi)/2) Gamma[1/r, (c - 2 I b k + I b m - p) z^r])/ ((c - 2 I b k + I b m - p) z^r)^r^(-1)), {k, 0, Floor[(1/2) (-1 + m)]}] /; Element[m, Integers] && m > 0










Standard Form





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MathML Form







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Date Added to functions.wolfram.com (modification date)





2002-12-18