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Sinh




Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Integration > Indefinite integration > Involving functions of the direct function and trigonometric functions > Involving powers of the direct function and trigonometric functions > Involving sec





http://functions.wolfram.com/01.19.21.2767.01









  


  








Input Form





Integrate[Sec[b z] Sinh[c z]^v, z] == -((I I^v 2^(1 - v) ArcTan[E^(I b z)] Binomial[v, v/2] (1 - Mod[v, 2]))/b) + 2^(1 - v) Sum[((-1)^k E^((I b - c (2 k + v)) z) Binomial[v, k] (E^(I Pi v + 4 c k z) (I b + c (-2 k + v)) Hypergeometric2F1[ (b - I (2 c k - c v))/(2 b), 1, (3 b - I (2 c k - c v))/(2 b), -E^(2 I b z)] + E^(2 c v z) (I b + 2 c k - c v) Hypergeometric2F1[(b + I (2 c k - c v))/(2 b), 1, (3 b + I (2 c k - c v))/(2 b), -E^(2 I b z)]))/ ((I b + 2 c k - c v) (I b + c (-2 k + v))), {k, 0, Floor[(1/2) (-1 + v)]}] /; Element[v, Integers] && v > 0








Standard Form





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MathML Form







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</apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2002-12-18