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http://functions.wolfram.com/01.21.21.0180.01
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Integrate[E^(p z) Sin[a z] Sinh[b z] Tanh[c z], z] ==
(1/4) I ((E^(((-I) a - b + p) z) Hypergeometric2F1[((-I) a - b + p)/(2 c),
1, 1 + ((-I) a - b + p)/(2 c), -E^(2 c z)])/((-I) a - b + p) -
(E^((I a - b + p) z) Hypergeometric2F1[(I a - b + p)/(2 c), 1,
1 + (I a - b + p)/(2 c), -E^(2 c z)])/(I a - b + p) -
(1/((-I) a + b + p)) (E^(((-I) a + b + p) z) Hypergeometric2F1[
((-I) a + b + p)/(2 c), 1, 1 + ((-I) a + b + p)/(2 c), -E^(2 c z)]) +
(E^((I a + b + p) z) Hypergeometric2F1[(I a + b + p)/(2 c), 1,
1 + (I a + b + p)/(2 c), -E^(2 c z)])/(I a + b + p) -
(E^(((-I) a - b + 2 c + p) z) Hypergeometric2F1[
1 + ((-I) a - b + p)/(2 c), 1, 2 + ((-I) a - b + p)/(2 c), -E^(2 c z)])/
((-I) a - b + 2 c + p) + (1/(I a - b + 2 c + p))
(E^((I a - b + 2 c + p) z) Hypergeometric2F1[1 + (I a - b + p)/(2 c), 1,
2 + (I a - b + p)/(2 c), -E^(2 c z)]) +
(E^(((-I) a + b + 2 c + p) z) Hypergeometric2F1[
1 + ((-I) a + b + p)/(2 c), 1, 2 + ((-I) a + b + p)/(2 c), -E^(2 c z)])/
((-I) a + b + 2 c + p) - (1/(I a + b + 2 c + p))
(E^((I a + b + 2 c + p) z) Hypergeometric2F1[1 + (I a + b + p)/(2 c), 1,
2 + (I a + b + p)/(2 c), -E^(2 c z)]))
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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> <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> a </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> b </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> tanh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> b </mi> </mrow> <mo> 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Date Added to functions.wolfram.com (modification date)
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