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http://functions.wolfram.com/01.07.21.2250.01
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Integrate[Sin[d z]/(a + b Sin[e z] + c Cos[e z])^2, z] ==
((1/(d - e)) (((-a) (a + Sqrt[a^2 - b^2 - c^2]) Hypergeometric2F1[1 - d/e,
1, 2 - d/e, (((-I) b + c) E^(I e z))/(-a + Sqrt[a^2 - b^2 - c^2])] +
a (a - Sqrt[a^2 - b^2 - c^2]) Hypergeometric2F1[1 - d/e, 1, 2 - d/e,
(I (b + I c) E^(I e z))/(a + Sqrt[a^2 - b^2 - c^2])] +
a^2 Hypergeometric2F1[1 - d/e, 2, 2 - d/e, (((-I) b + c) E^(I e z))/
(-a + Sqrt[a^2 - b^2 - c^2])] - b^2 Hypergeometric2F1[1 - d/e, 2,
2 - d/e, (((-I) b + c) E^(I e z))/(-a + Sqrt[a^2 - b^2 - c^2])] -
c^2 Hypergeometric2F1[1 - d/e, 2, 2 - d/e, (((-I) b + c) E^(I e z))/
(-a + Sqrt[a^2 - b^2 - c^2])] + a Sqrt[a^2 - b^2 - c^2]
Hypergeometric2F1[1 - d/e, 2, 2 - d/e, (((-I) b + c) E^(I e z))/
(-a + Sqrt[a^2 - b^2 - c^2])] - a^2 Hypergeometric2F1[1 - d/e, 2,
2 - d/e, (I (b + I c) E^(I e z))/(a + Sqrt[a^2 - b^2 - c^2])] +
b^2 Hypergeometric2F1[1 - d/e, 2, 2 - d/e, (I (b + I c) E^(I e z))/
(a + Sqrt[a^2 - b^2 - c^2])] + c^2 Hypergeometric2F1[1 - d/e, 2,
2 - d/e, (I (b + I c) E^(I e z))/(a + Sqrt[a^2 - b^2 - c^2])] +
a Sqrt[a^2 - b^2 - c^2] Hypergeometric2F1[1 - d/e, 2, 2 - d/e,
(I (b + I c) E^(I e z))/(a + Sqrt[a^2 - b^2 - c^2])])/
E^(I (d - e) z)) + (1/(d + e)) (E^(I (d + e) z)
((-a) (a + Sqrt[a^2 - b^2 - c^2]) Hypergeometric2F1[(d + e)/e, 1,
2 + d/e, (((-I) b + c) E^(I e z))/(-a + Sqrt[a^2 - b^2 - c^2])] +
a (a - Sqrt[a^2 - b^2 - c^2]) Hypergeometric2F1[(d + e)/e, 1, 2 + d/e,
(I (b + I c) E^(I e z))/(a + Sqrt[a^2 - b^2 - c^2])] +
a^2 Hypergeometric2F1[(d + e)/e, 2, 2 + d/e, (((-I) b + c) E^(I e z))/
(-a + Sqrt[a^2 - b^2 - c^2])] - b^2 Hypergeometric2F1[(d + e)/e, 2,
2 + d/e, (((-I) b + c) E^(I e z))/(-a + Sqrt[a^2 - b^2 - c^2])] -
c^2 Hypergeometric2F1[(d + e)/e, 2, 2 + d/e, (((-I) b + c) E^(I e z))/
(-a + Sqrt[a^2 - b^2 - c^2])] + a Sqrt[a^2 - b^2 - c^2]
Hypergeometric2F1[(d + e)/e, 2, 2 + d/e, (((-I) b + c) E^(I e z))/
(-a + Sqrt[a^2 - b^2 - c^2])] - a^2 Hypergeometric2F1[(d + e)/e, 2,
2 + d/e, (I (b + I c) E^(I e z))/(a + Sqrt[a^2 - b^2 - c^2])] +
b^2 Hypergeometric2F1[(d + e)/e, 2, 2 + d/e, (I (b + I c) E^(I e z))/
(a + Sqrt[a^2 - b^2 - c^2])] + c^2 Hypergeometric2F1[(d + e)/e, 2,
2 + d/e, (I (b + I c) E^(I e z))/(a + Sqrt[a^2 - b^2 - c^2])] +
a Sqrt[a^2 - b^2 - c^2] Hypergeometric2F1[(d + e)/e, 2, 2 + d/e,
(I (b + I c) E^(I e z))/(a + Sqrt[a^2 - b^2 - c^2])])))/
(2 (I b + c) (a^2 - b^2 - c^2)^(3/2))
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</mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mrow> <mo> - </mo> <mi> ⅈ </mi> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> d </mi> <mo> - </mo> <mi> e </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mn> 2 </mn> </msub> <msub> <mi> F </mi> <mn> 1 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <mi> d </mi> <mi> e </mi> </mfrac> </mrow> <mo> , </mo> <mn> 2 </mn> </mrow> <mo> ; </mo> <mrow> <mn> 2 </mn> <mo> - </mo> <mfrac> <mi> d </mi> <mi> e </mi> </mfrac> </mrow> <mo> ; </mo> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> c </mi> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> b </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> e </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> </mrow> <mrow> <msqrt> 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<mi> c </mi> </mrow> </mrow> <mtext> </mtext> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> e </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> </mrow> <mrow> <mi> a </mi> <mo> + </mo> <msqrt> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> - </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> - </mo> <msup> <mi> c </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["1", "-", FractionBox["d", "e"]]], Hypergeometric2F1], ",", TagBox["2", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[RowBox[List["2", "-", FractionBox["d", 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</semantics> </math>
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