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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 sin and exp > Involving eb zr+d z+e sin(a zr+p z+q) sinh(c zr+f z+g)





http://functions.wolfram.com/01.19.21.1202.01









  


  










Input Form





Integrate[E^(b z^2 + d z + e) Sin[a z^2 + p z + q] Sinh[c z^2 + f z + g], z] == (1/8) (-1)^(1/4) E^(e - g - I q) Sqrt[Pi] (-((I Erfi[((-1)^(1/4) (d - f - I p - 2 I a z + 2 b z - 2 c z))/ (2 Sqrt[a + I (b - c)])])/ (E^((I (-d + f + I p)^2)/(4 (a + I (b - c)))) Sqrt[a + I (b - c)])) - (E^((1/4) I ((d - f + I p)^2/(a - I b + I c) + 8 q)) Erfi[((-1)^(3/4) (d - f + I p + 2 I a z + 2 b z - 2 c z))/ (2 Sqrt[a - I b + I c])])/Sqrt[a - I b + I c] + E^(2 g) ((8 Sqrt[a + I (b + c)] Erfi[((-1)^(3/4) (I d + I f + p + 2 a z + 2 I b z + 2 I c z))/(2 Sqrt[a + I (b + c)])])/ E^((I (d + f - I p)^2)/(4 (a + I (b + c))))/(8 I a - 8 (b + c)) + (E^((1/4) I ((d + f + I p)^2/(a - I (b + c)) + 8 q)) Erfi[((-1)^(3/4) (d + f + I p + 2 I a z + 2 b z + 2 c z))/ (2 Sqrt[a - I (b + c)])])/Sqrt[a - I (b + c)]))










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