Let $(a, b)$ be the point of intersection of the curve $x^2=2 y$ and the straight line $y-2 x-6=0$ in the second quadrant. Then the integral $\mathrm{I}=\int_{\mathrm{a}}^{\mathrm{b}} \frac{9 x^2}{1+5^x} \mathrm{~d} x$ is equal to :

$4 \int_0^1\left(\frac{1}{\sqrt{3+x^2}+\sqrt{1+x^2}}\right) d x-3 \log _e(\sqrt{3})$ is equal to :

Let $f(x)=\int\limits_0^x \mathrm{t}\left(\mathrm{t}^2-9 \mathrm{t}+20\right) \mathrm{dt}, 1 \leq x \leq 5$. If the range of $f$ is $[\alpha, \beta]$, then $4(\alpha+\beta)$ equals :