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Sinh






Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Arguments involving polynomials or algebraic functions and power factors > Involving power > Involving zn sinh(c zr+f z)





http://functions.wolfram.com/01.19.21.0450.01









  


  










Input Form





Integrate[z^n Sinh[c z^2 + f z], z] == (2^(-2 - n) c^(-1 - n) (-f)^n (f + 2 c z) (-Sum[(-((f + 2 c z)^2/c))^((1/2) (-1 - j)) (-2 - (4 c z)/f)^j Binomial[n, j] Gamma[(1 + j)/2, -((f + 2 c z)^2/(4 c))], {j, 0, n}] + E^(f^2/(2 c)) Sum[((f + 2 c z)^2/c)^((1/2) (-1 - j)) (-2 - (4 c z)/f)^j Binomial[n, j] Gamma[(1 + j)/2, (f + 2 c z)^2/(4 c)], {j, 0, n}]))/ E^(f^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