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 Cos

 http://functions.wolfram.com/01.07.21.2703.01

 Input Form

 Integrate[E^(p z) Sin[d z] (a Sin[e z]^2 + b Cos[e z]^2)^\[Beta], z] == -((2^(-1 - 2 \[Beta]) (((-a) (-1 + E^(2 I e z))^2 + b (1 + E^(2 I e z))^2)/ E^(2 I e z))^\[Beta] (E^((I d + p) z) (d + I p + 2 e \[Beta]) AppellF1[(d - I p - 2 e \[Beta])/(2 e), -\[Beta], -\[Beta], (d + 2 e - I p - 2 e \[Beta])/(2 e), ((a - b) E^(2 I e z))/ (a + b + 2 Sqrt[a b]), ((a - b) E^(2 I e z))/ (a + b - 2 Sqrt[a b])] + E^(((-I) d + p) z) (d - I p - 2 e \[Beta]) AppellF1[-((d + I p + 2 e \[Beta])/(2 e)), -\[Beta], -\[Beta], -((d + I p + 2 e (-1 + \[Beta]))/(2 e)), ((a - b) E^(2 I e z))/ (a + b + 2 Sqrt[a b]), ((a - b) E^(2 I e z))/ (a + b - 2 Sqrt[a b])]))/ ((1 + ((-a + b) E^(2 I e z))/(a + b - 2 Sqrt[a b]))^\[Beta] (1 + ((-a + b) E^(2 I e z))/(a + b + 2 Sqrt[a b]))^\[Beta]))/ (d^2 + (p - 2 I e \[Beta])^2)

 Standard Form

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RowBox[List["(", RowBox[List[SuperscriptBox["d", "2"], "+", SuperscriptBox[RowBox[List["(", RowBox[List["p", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "e", " ", "\[Beta]"]]]], ")"]], "2"]]], ")"]]]]]]]]

 MathML Form

 p z sin ( d z ) ( a sin 2 ( e z ) + b cos 2 ( e z ) ) β z - 1 d 2 + ( p - 2 e β ) 2 ( 2 - 2 β - 1 ( 2 e z ( b - a ) a + b - 2 a b + 1 ) - β ( 2 e z ( b - a ) a + b + 2 a b + 1 ) - β ( - 2 e z ( b ( 1 + 2 e z ) 2 - a ( - 1 + 2 e z ) 2 ) ) β ( ( d + p ) z ( d + p + 2 e β ) F 1 AppellF1 ( d - p - 2 e β 2 e ; - β , - β ; d + 2 e - p - 2 e β 2 e ; ( a - b ) 2 e z a + b + 2 a b , ( a - b ) 2 e z a + b - 2 a b ) + ( - d + p ) z ( d - p - 2 e β ) F 1 AppellF1 ( - d + p + 2 e β 2 e ; - β , - β ; - d + p + 2 e ( β - 1 ) 2 e ; ( a - b ) 2 e z a + b + 2 a b , ( a - b ) 2 e z a + b - 2 a b ) ) ) z p z d z a e z 2 b e z 2 β -1 1 d 2 p -1 2 e β 2 -1 2 -2 β -1 2 e z b -1 a a b -1 2 a b 1 2 -1 1 -1 β 2 e z b -1 a a b 2 a b 1 2 -1 1 -1 β -2 e z b 1 2 e z 2 -1 a -1 2 e z 2 β d p z d p 2 e β AppellF1 d -1 p -1 2 e β 2 e -1 -1 β -1 β d 2 e -1 p -1 2 e β 2 e -1 a -1 b 2 e z a b 2 a b 1 2 -1 a -1 b 2 e z a b -1 2 a b 1 2 -1 -1 d p z d -1 p -1 2 e β AppellF1 -1 d p 2 e β 2 e -1 -1 β -1 β -1 d p 2 e β -1 2 e -1 a -1 b 2 e z a b 2 a b 1 2 -1 a -1 b 2 e z a b -1 2 a b 1 2 -1 [/itex]

 Rule Form

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

 2002-12-18