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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 powers of the direct function and exponential function > Involving powers of sin and exp > Involving eb zr+d zsinv(c z)





http://functions.wolfram.com/01.06.21.1280.01









  


  










Input Form





Integrate[E^(b Sqrt[z] + d z) Sin[c z]^v, z] == (Binomial[v, v/2] (E^(b Sqrt[z] + d z)/d - (b Sqrt[Pi] Erfi[(b + 2 d Sqrt[z])/(2 Sqrt[d])])/ (E^(b^2/(4 d)) (2 d^(3/2)))) (1 - Mod[v, 2]))/2^v + Sum[(-1)^s Binomial[v, s] (E^(b Sqrt[z]) (((-1)^v E^((d + 2 I c s - I c v) z))/(d + 2 I c s - I c v) + E^((d - 2 I c s + I c v) z)/(d - 2 I c s + I c v)) - ((-1)^v b E^(b^2/(-4 d - 8 I c s + 4 I c v)) Sqrt[Pi] Erfi[(b + 2 (d + 2 I c s - I c v) Sqrt[z])/ (2 Sqrt[d + 2 I c s - I c v])])/(2 (d + 2 I c s - I c v)^(3/2)) - (b E^(b^2/(-4 d + 8 I c s - 4 I c v)) Sqrt[Pi] Erfi[(b + 2 (d - 2 I c s + I c v) Sqrt[z])/ (2 Sqrt[d - 2 I c s + I c v])])/(2 (d - 2 I c s + I c v)^(3/2))), {s, 0, Floor[(1/2) (-1 + v)]}]/(2^v I^v) /; 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