If a particle moves such that the displacement (s) is proportional to the square of the velocity (v), then its acceleration (a) is

If $\int e^{x + \tan^{-1}x}\left(\dfrac{x^2 + 2}{\sec^2(\tan^{-1}x)}\right)dx = e^{f(x)} + c$, then $\ldots$

Let $f(x) = x$, $f_1(x) = f(\log x)$, $f_2(x) = f_1(\log x)$, $f_3(x) = f_2(\log x)$, $\ldots$ and so on. Then $\int \dfrac{1}{f(x)\,f_1(x)\,f_2(x)\,\ldots f_{2026}(x)}\,dx = \ldots$

If $\int_0^2 x(2 - x)^b\,dx = \dfrac{32}{7}$, where $b \in N$ then $b = $