Typical Indefinite Integration #2

Calculus Level 5

dx(x1)2012(x+1)20142013 \Large {\int} \large \frac{dx}{\sqrt[2013]{(x-1)^{2012} (x+1)^{2014}}}

Given that the integral above is defined for x>1x > 1. Ignoring the arbitrary constant, it evaluates to αβ(xλx+μ)σ/θ\large{ \frac{ \alpha}{\beta} \left( \frac{x - \lambda}{x + \mu} \right)^{\sigma / \theta }} where α,β,λ,μ,σ,θ\alpha, \beta, \lambda, \mu, \sigma, \theta are positive integers with gcd(α,β)=gcd(σ,θ)=1 \gcd(\alpha, \beta) = \gcd(\sigma, \theta ) = 1 . Find the value of α+β+λ+μ+σ+θ+6033\alpha+ \beta+ \lambda+ \mu+ \sigma+ \theta + 6033.

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