If \( a \neq b \) and \( a f(x)+b f\left(\frac{1}{x}\right)=\frac{1}{x}-5 \) for all \( x \neq 0....

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If \( a \neq b \) and \( a f(x)+b f\left(\frac{1}{x}\right)=\frac{1}{x}-5 \) for all \( x \neq 0 \), then
\( \mathrm{P} \)
\( \int_{1}^{2} f(x) d x=\frac{1}{a^{2}-b^{2}}\left[a(\log 2-\alpha)+\beta\left(\frac{b}{2}\right)\right] \)
Where \( \beta-\alpha \) is equal to
(1) 12
(2) 5
(3) 7
(4) 2
.


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