Cho hàm số $f\left( x \right)=\left\{ \begin{aligned} &...

+ Đặt

+ Đặt $$
$\Rightarrow \int\limits_{0}^{\frac{\pi }{2}}{f\left( 2\sin x-1 \right)}.\cos x\text{d}x+\int\limits_{e}^{{{e}^{2}}}{\frac{f\left( \ln x \right)}{x}}=\frac{23}{4}\Rightarrow a=23,b=4\Rightarrow a.b=92$.
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