Calculust 7

Calculus Level 4

11+52x2+1x4x2+1ln(1+x1x)dx \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 πaln(b)\dfrac{\pi}{a}\ln(b) , where aa and bb are positive integers, with bb minimized. What is the value of a+ba+b?

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