Trying to mix some concepts!

Calculus Level 4

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

8 2 0 5

Prashant Kr by Prashant Kr , 22, India

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