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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 and exponential functions > Involving cos and algebraic functions of exp > Involving (a+b ed z)beta cos(e z)sinh(c z)





http://functions.wolfram.com/01.19.21.1281.01









  


  








Input Form





Integrate[(a + b E^(d z))^\[Beta] Cos[e z] Sinh[c z], z] == ((-(1/4)) (a + b E^(d z))^\[Beta] ((1/(-c + I e)) (E^((c - I e) z) Hypergeometric2F1[(c - I e)/d, -\[Beta], (c + d - I e)/d, -((b E^(d z))/a)] + E^((-c + I e) z) Hypergeometric2F1[(-c + I e)/d, -\[Beta], (-c + d + I e)/d, -((b E^(d z))/a)]) + (1/(-c - I e)) (E^((-c - I e) z) Hypergeometric2F1[(-c - I e)/d, -\[Beta], (-c + d - I e)/d, -((b E^(d z))/a)] + E^((c + I e) z) Hypergeometric2F1[(c + I e)/d, -\[Beta], (c + d + I e)/d, -((b E^(d z))/a)])))/(1 + (b E^(d z))/a)^\[Beta]








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