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Sinh






Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving rational functions > Involving (a z2+b z+c)-n





http://functions.wolfram.com/01.19.21.0155.01









  


  










Input Form





Integrate[Sinh[d z]/(a z^2 + b z + c)^2, z] == (1/(b^2 - 4 a c)^(3/2)) ((1/(c + z (b + a z))) ((c + z (b + a z)) (CosIntegral[(I d (b - Sqrt[b^2 - 4 a c] + 2 a z))/ (2 a)] (Sqrt[b^2 - 4 a c] d Cosh[((b - Sqrt[b^2 - 4 a c]) d)/ (2 a)] + 2 a Sinh[((b - Sqrt[b^2 - 4 a c]) d)/(2 a)]) + CosIntegral[(I d (b + Sqrt[b^2 - 4 a c] + 2 a z))/(2 a)] (Sqrt[b^2 - 4 a c] d Cosh[((b + Sqrt[b^2 - 4 a c]) d)/(2 a)] - 2 a Sinh[((b + Sqrt[b^2 - 4 a c]) d)/(2 a)])) - Sqrt[b^2 - 4 a c] (b + 2 a z) Sinh[d z]) - (2 a Cosh[((b - Sqrt[b^2 - 4 a c]) d)/(2 a)] + Sqrt[b^2 - 4 a c] d Sinh[((b - Sqrt[b^2 - 4 a c]) d)/(2 a)]) SinhIntegral[(d (b - Sqrt[b^2 - 4 a c] + 2 a z))/(2 a)] + (2 a Cosh[((b + Sqrt[b^2 - 4 a c]) d)/(2 a)] - Sqrt[b^2 - 4 a c] d Sinh[((b + Sqrt[b^2 - 4 a c]) d)/(2 a)]) SinhIntegral[(d (b + Sqrt[b^2 - 4 a c] + 2 a z))/(2 a)])










Standard Form





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MathML Form







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





2002-12-18