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Sin






Mathematica Notation

Traditional Notation









Elementary Functions > Sin[z] > Integration > Indefinite integration > Involving functions of the direct function and exponential function > Involving products of powers of two direct functions and exponential function > Involving product of power of the direct function, the direct function and algebraic functions of exp > Involving (a+b ed z)beta sin(e z)sinv(c z)





http://functions.wolfram.com/01.06.21.1402.01









  


  










Input Form





Integrate[(a + b E^(d z))^\[Beta] Sin[e z] Sin[c z]^v, z] == (-(1/e)) ((2^(-1 - v) (a + b E^(d z))^\[Beta] Binomial[v, v/2] (Hypergeometric2F1[-((I e)/d), -\[Beta], (d - I e)/d, -((b E^(d z))/a)]/ E^(I e z) + E^(I e z) Hypergeometric2F1[(I e)/d, -\[Beta], (d + I e)/d, -((b E^(d z))/a)]) (1 - Mod[v, 2]))/ (1 + (b E^(d z))/a)^\[Beta]) + (2^(-1 - v) (a + b E^(d z))^\[Beta] Sum[(-1)^s Binomial[v, s] (Sin[(v Pi)/2] (((-E^((I e + 2 I c s - I c v) z)) Hypergeometric2F1[ (I e + 2 I c s - I c v)/d, -\[Beta], (d + I e + 2 I c s - I c v)/ d, -((b E^(d z))/a)] + E^(((-I) e - 2 I c s + I c v) z) Hypergeometric2F1[((-I) e - 2 I c s + I c v)/d, -\[Beta], (d - I e - 2 I c s + I c v)/d, -((b E^(d z))/a)])/ ((-I) e - 2 I c s + I c v)) - Sin[(v Pi)/2] ((E^(((-I) e + 2 I c s - I c v) z) Hypergeometric2F1[ ((-I) e + 2 I c s - I c v)/d, -\[Beta], (d - I e + 2 I c s - I c v)/d, -((b E^(d z))/a)] - E^((I e - 2 I c s + I c v) z) Hypergeometric2F1[(I e - 2 I c s + I c v)/d, -\[Beta], (d + I e - 2 I c s + I c v)/d, -((b E^(d z))/a)])/ ((-I) e + 2 I c s - I c v)) + Cos[(Pi v)/2] ((E^((I e + 2 I c s - I c v) z) Hypergeometric2F1[ (I e + 2 I c s - I c v)/d, -\[Beta], (d + I e + 2 I c s - I c v)/ d, -((b E^(d z))/a)] + E^(((-I) e - 2 I c s + I c v) z) Hypergeometric2F1[((-I) e - 2 I c s + I c v)/d, -\[Beta], (d - I e - 2 I c s + I c v)/d, -((b E^(d z))/a)])/ (-e - 2 c s + c v)) + Cos[(Pi v)/2] ((E^(((-I) e + 2 I c s - I c v) z) Hypergeometric2F1[ ((-I) e + 2 I c s - I c v)/d, -\[Beta], (d - I e + 2 I c s - I c v)/d, -((b E^(d z))/a)] + E^((I e - 2 I c s + I c v) z) Hypergeometric2F1[(I e - 2 I c s + I c v)/d, -\[Beta], (d + I e - 2 I c s + I c v)/d, -((b E^(d z))/a)])/ (-e + 2 c s - c v))), {s, 0, Floor[(1/2) (-1 + v)]}])/ (1 + (b E^(d z))/a)^\[Beta] /; Element[v, Integers] && v > 0










Standard Form





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MathML Form







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





2002-12-18