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

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SUMMARY

The forum discussion centers on the evaluation of the definite integral $$\int^{\frac{\sqrt{5}+1}{2}}_{1}\frac{x^2+1}{x^4-x^2+1}\ln\left(x-\frac{1}{x}+1\right)dx$$. Participants explore various methods for solving this integral, including substitution techniques and numerical integration. The discussion highlights the complexity of the integrand and the necessity for advanced calculus methods to achieve a solution.

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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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