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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 inverse trigonometric functions > Involving tan-1





http://functions.wolfram.com/01.19.21.0431.01









  


  








Input Form





Integrate[Sinh[a ArcTan[z]], z] == (1/(2 (4 + a^2))) (((2 + I a) a E^(2 (I + a) ArcTan[z]) Hypergeometric2F1[1 - (I a)/2, 1, 2 - (I a)/2, -E^(2 I ArcTan[z])] + (2 I + a) ((-I) a E^(2 I ArcTan[z]) Hypergeometric2F1[1 + (I a)/2, 1, 2 + (I a)/2, -E^(2 I ArcTan[z])] + (-2 I + a) ((-1 + E^(2 a ArcTan[z])) z - I E^(2 a ArcTan[z]) Hypergeometric2F1[-((I a)/2), 1, 1 - (I a)/2, -E^(2 I ArcTan[z])] + I Hypergeometric2F1[(I a)/2, 1, 1 + (I a)/2, -E^(2 I ArcTan[z])])))/ E^(a ArcTan[z]))








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