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Sin




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.06.21.1611.01









  


  








Input Form





Integrate[(a + b z)^\[Beta] d^z Sin[c z] Sin[e z], z] == ((-(1/4)) I (a + b z)^\[Beta] ((1/(c - e - I Log[d])) ((Gamma[1 + \[Beta], -((I (a + b z) (c - e - I Log[d]))/b)] (Cos[(a (c - e))/b] - I Sin[(a (c - e))/b]))/ (-((I (a + b z) (c - e - I Log[d]))/b))^\[Beta]) - (1/b) (I (a + b z) Gamma[1 + \[Beta], (I (a + b z) (c - e + I Log[d]))/b] ((I (a + b z) (c - e + I Log[d]))/b)^(-1 - \[Beta]) (Cos[(a (c - e))/b] + I Sin[(a (c - e))/b])) - (1/(c + e - I Log[d])) ((Gamma[1 + \[Beta], -((I (a + b z) (c + e - I Log[d]))/b)] (Cos[(a (c + e))/b] - I Sin[(a (c + e))/b]))/ (-((I (a + b z) (c + e - I Log[d]))/b))^\[Beta]) + (1/(c + e + I Log[d])) ((Gamma[1 + \[Beta], (I (a + b z) (c + e + I Log[d]))/b] (Cos[(a (c + e))/b] + I Sin[(a (c + e))/b]))/ ((I (a + b z) (c + e + I Log[d]))/b)^\[Beta])))/d^(a/b)








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