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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 cos, exp and power > Involving znep z cos(b z)sinh(c zr)





http://functions.wolfram.com/01.19.21.1413.01









  


  










Input Form





Integrate[z^n E^(p z) Cos[b z] Sinh[c z^2], z] == (2^(-4 - n) (-c)^(-n - 1) (E^((p (2 I b + 3 p))/(4 c)) Sum[(I b - p)^(n - q) ((-I) b + p - 2 c z)^(1 + q) Binomial[n, q] ExpIntegralE[(1 - q)/2, ((-I) b + p - 2 c z)^2/(4 c)], {q, 0, n}] + 2^n E^((3 p (2 I b + p))/(4 c)) Sum[(((-I) b - p)^(n - q) (I b + p - 2 c z)^(1 + q) Binomial[n, q] ExpIntegralE[(1 - q)/2, (I b + p - 2 c z)^2/(4 c)])/2^n, {q, 0, n}] + (-1)^n E^((2 b^2 + 2 I b p + p^2)/(4 c)) (2^n Sum[(((-I) b - p)^(n - q) (I b + p + 2 c z)^(1 + q) Binomial[n, q] ExpIntegralE[(1 - q)/2, -((I b + p + 2 c z)^2/(4 c))])/2^n, {q, 0, n}] + E^((I b p)/c) Sum[(I b - p)^(n - q) ((-I) b + p + 2 c z)^(1 + q) Binomial[n, q] ExpIntegralE[(1 - q)/2, (b + I (p + 2 c z))^2/(4 c)], {q, 0, n}])))/ E^((b^2 + 4 I b p + 2 p^2)/(4 c)) /; Element[n, Integers] && n >= 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