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integrate


Integrate[(BesselJ[0, x]*Log[x])/Sqrt[1 + x^2], {x, 1, Infinity}]
Integrate[(BesselJ[0, x]*Log[x])/Sqrt[1 + x^2], {x, 1, Infinity}]

NIntegrate[(BesselJ[0, x]*Log[x])/Sqrt[1 + x^2], {x, 1, Infinity},
Method -> Oscillatory]
-0.06630573213061997

Integrate[(BesselK[0, x]*BesselY[1, x])/Sqrt[1 + x^2], {x, 1,
Infinity}]
Integrate[(BesselK[0, x]*BesselY[1, x])/Sqrt[1 + x^2], {x, 1,
Infinity}]

NIntegrate[(BesselK[0, x]*BesselY[1, x])/Sqrt[1 + x^2], {x, 1,
Infinity}]
-0.06586252709607003

------->   Any possibility to get closed form results within
Mathematica?

Integrate[Sqrt[x^2 + 1]/Sqrt[1 + x^6], {x, 0, 10}]
(-(-1)^(1/6))*EllipticF[I*ArcSinh[10*(-1)^(1/3)], (-1)^(2/3)]

N[%]
-0.10016641038463325 - 1.6857503548125956*I

NIntegrate[Sqrt[x^2 + 1]/Sqrt[1 + x^6], {x, 0, 10}]
2.056349237110889

--------> Any ideas to "help" Mathematica to give a correct answer?

Regards
Dimitris


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