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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, exponential and a power functions > Involving powers of cos, exp and power > Involving zalpha-1 eb zr+e cosm(a zr+q) sinh(c zr+g)





http://functions.wolfram.com/01.19.21.1452.01









  


  










Input Form





Integrate[z^n E^(b Sqrt[z] + e) Cos[a Sqrt[z] + q]^m Sinh[c Sqrt[z] + g], z] == (Binomial[m, m/2] ((-(-b - c)^(-2 (1 + n))) E^(e + g) Gamma[2 (1 + n), (-b - c) Sqrt[z]] + (E^(e - g) Gamma[2 (1 + n), (-b + c) Sqrt[z]])/(-b + c)^(2 (1 + n))) (1 - Mod[m, 2]))/2^m - Sum[Binomial[m, s] ((E^(e + g + I q (m - 2 s)) Gamma[2 (1 + n), (-b - c - I a (m - 2 s)) Sqrt[z]])/(-b - c - I a (m - 2 s))^ (2 (1 + n)) - (E^(e - g + I q (m - 2 s)) Gamma[2 (1 + n), (-b + c - I a (m - 2 s)) Sqrt[z]])/(-b + c - I a (m - 2 s))^ (2 (1 + n)) + (E^(e + g - I q (m - 2 s)) Gamma[2 (1 + n), (-b - c + I a (m - 2 s)) Sqrt[z]])/(-b - c + I a (m - 2 s))^ (2 (1 + n)) - (E^(e - g - I q (m - 2 s)) Gamma[2 (1 + n), (-b + c + I a (m - 2 s)) Sqrt[z]])/(-b + c + I a (m - 2 s))^ (2 (1 + n))), {s, 0, Floor[(1/2) (-1 + m)]}]/2^m /; Element[m, Integers] && m > 0 && Element[n, Integers] && n >= 0










Standard Form





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MathML Form







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





2002-12-18