Let $f(x)$ be a real valued $f$ unction which is monotonic and differentiable. Then for any reals a and $b, \int_{f(a)}^{f(b)} 2 x\left\{b-f^{-1}(x)\right\} d x=$

Let $a, b, c$ be non-zero real numbers, such that $\int_0^r\left(1+\cos ^8 x\right)\left(a x^2+b x+c\right) d x=\int_0^{2^{\prime}}\left(1+\cos ^8 x\right)\left(a x^2+b x+c\right) d x$, then $a x^2+b x+c=0$ has

The value of the integral $\int\limits_3^6 \frac{\sqrt{x}}{\sqrt{9-x}+\sqrt{x}} d x$ is

$\int_\limits{-1}^1 \frac{x^3+|x|+1}{x^2+2|x|+1} d x$ is equal to