# Trying to mix some concepts!

Calculus Level pending

Consider$f(x) =4x^{4} -24x^3+31x^2 +6x-8$ be a polynomial function and $$\alpha ,\beta,\gamma, \delta$$ are the roots of the equation $$f(x)=0$$. If it is known that sum of any two out of $$\alpha ,\beta ,\gamma ,\delta$$ vanishes then compute $\large \int_{2\alpha}^{2\beta}\dfrac{x^{\delta+1}-6x^{\gamma+1}+2\beta|x|+1}{x^2+4\beta|x|+1} \, dx .$

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