How to integrate $\int_0^{+\infty} \frac{x^2\ln x}{x^4-x^3+1}\,\mathrm{d}x$?

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First I think it may use the method of contour integration,but I have no idea how to create a contour.And is there some normal method to solve it? $$\int_0^{+\infty} \frac{x^2\ln x}{x^4-x^3+1}\,\mathrm{d}x$$