An interesting integral

Calculus Level 2

0ln1+x111+x3(1+x2)lnxdx=?\large \int_0^\infty\frac{\ln\frac{1+x^{11}}{1+x^3}}{(1+x^2)\ln x}\, \mathrm dx = \, ?

The integral above has a closed form. Evaluate this integral and give your answer to three decimal places.

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