Typical Indefinite Integration #2

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

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