If for nonzero $$x$$, $$af(x)+$$ $$bf\left( {{1 \over x}} \right) = {1 \over x} - 5$$ where $$a \ne b,$$ then
$$\int_1^2 {f\left( x \right)dx} = .......$$
Answer
$${1 \over {{a^2} - {b^2}}}\left[ {a\left( {\log 2 - 5} \right) + {{7b} \over 2}} \right]$$