MHB Definite Integration: $$\int^{\frac{\sqrt{5}+1}{2}}_{1}$$

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Evaluation of $$\int^{\frac{\sqrt{5}+1}{2}}_{1}\frac{x^2+1}{x^4-x^2+1}\ln\left(x-\frac{1}{x}+1\right)dx$$
 
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What methods are expected to use ? what have you tried so far ?
 

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