# Calculust 7

Calculus Level 4

$\large \int_{1}^{\frac{1+\sqrt{5}}{2}} \dfrac{x^2+1}{x^4-x^2+1} \ln\left( 1+x-\dfrac{1}{x} \right) \, dx$

The above expression can be expressed as $$\dfrac{\pi}{a}\ln(b)$$, where $$a$$ and $$b$$ are positive integers, with $$b$$ minimized. What is the value of $$a+b$$?

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