If ∫₀¹1/(5+2x-2x²)(1+e^(2-4x)) dx =1/αlogₑ ((α+1)/β), α,β>0, then… | JEE Main 2023 Mathematics PYQ

MCQMediumJEE Main 2023 · 15 April, Shift 1Properties of Definite Integrals

If $\int_{0}^{1}\frac{1}{(5+2x-2x^2)\big(1+e^{(2-4x)}\big)}\,dx =\frac{1}{\alpha}\log_e\!\left(\frac{\alpha+1}{\beta}\right), \quad \alpha,\beta>0,$ then $\alpha^{4}-\beta^{4}$ is equal to

A
$-21$
B
$0$
C
$19$
D
$21$

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