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http://functions.wolfram.com/01.07.21.2656.01
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Integrate[(E^(p z) Sin[d z])/(a + b Cos[c z]^2)^2, z] ==
(I (-((1/(2 I c - I d + p)) (E^((2 I c - I d + p) z)
((-(2 a + b)) (2 a + b + 2 Sqrt[a] Sqrt[a + b]) Hypergeometric2F1[
1 - (d + I p)/(2 c), 1, 2 - (d + I p)/(2 c),
-((b E^(2 I c z))/(2 a + b - 2 Sqrt[a] Sqrt[a + b]))] -
(2 a + b) (-2 a - b + 2 Sqrt[a] Sqrt[a + b]) Hypergeometric2F1[
1 - (d + I p)/(2 c), 1, 2 - (d + I p)/(2 c),
-((b E^(2 I c z))/(2 a + b + 2 Sqrt[a] Sqrt[a + b]))] +
2 Sqrt[a] ((2 a^(3/2) + 2 Sqrt[a] b + 2 a Sqrt[a + b] +
b Sqrt[a + b]) Hypergeometric2F1[1 - (d + I p)/(2 c), 2,
2 - (d + I p)/(2 c), -((b E^(2 I c z))/(2 a + b - 2 Sqrt[a]
Sqrt[a + b]))] + (-2 a^(3/2) - 2 Sqrt[a] b +
2 a Sqrt[a + b] + b Sqrt[a + b]) Hypergeometric2F1[
1 - (d + I p)/(2 c), 2, 2 - (d + I p)/(2 c),
-((b E^(2 I c z))/(2 a + b + 2 Sqrt[a] Sqrt[a + b]))])))) +
(1/(2 I c + I d + p)) (E^((2 I c + I d + p) z)
((-(2 a + b)) (2 a + b + 2 Sqrt[a] Sqrt[a + b]) Hypergeometric2F1[
(2 c + d - I p)/(2 c), 1, (4 c + d - I p)/(2 c),
-((b E^(2 I c z))/(2 a + b - 2 Sqrt[a] Sqrt[a + b]))] -
(2 a + b) (-2 a - b + 2 Sqrt[a] Sqrt[a + b]) Hypergeometric2F1[
(2 c + d - I p)/(2 c), 1, (4 c + d - I p)/(2 c),
-((b E^(2 I c z))/(2 a + b + 2 Sqrt[a] Sqrt[a + b]))] +
2 Sqrt[a] ((2 a^(3/2) + 2 Sqrt[a] b + 2 a Sqrt[a + b] + b Sqrt[a + b])
Hypergeometric2F1[(2 c + d - I p)/(2 c), 2, (4 c + d - I p)/(2 c),
-((b E^(2 I c z))/(2 a + b - 2 Sqrt[a] Sqrt[a + b]))] +
(-2 a^(3/2) - 2 Sqrt[a] b + 2 a Sqrt[a + b] + b Sqrt[a + b])
Hypergeometric2F1[(2 c + d - I p)/(2 c), 2, (4 c + d - I p)/(2 c),
-((b E^(2 I c z))/(2 a + b + 2 Sqrt[a] Sqrt[a + b]))])))))/
(4 a^(3/2) b (a + b)^(3/2))
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mo> ∫ </mo> <mrow> <mfrac> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mi> p </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> d </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mrow> <mi> b </mi> <mo> ⁢ </mo> <mrow> <msup> <mi> cos </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msup> <mi> a </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mrow> 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<cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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Date Added to functions.wolfram.com (modification date)
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