The value of $c$ satisfied by the Rolle's theorem for the function $f(x) = x^2(1 - x)^2$, $x \in [0, 1]$ is...

The value of integral $\displaystyle\int \dfrac{dx}{\sin^2 x + \tan^2 x}$ is...

The value of integral $\displaystyle\int \dfrac{\sqrt{x^2 + 1}\,[\log(x^2 + 1) - 2\log x]}{x^4}\,dx$ is equal to...

If $f(x) = \dfrac{1}{\log x}$ and $g(x) = \dfrac{1}{(\log x)^2}$, then the value of $\displaystyle\int [f(x) - g(x)]\,dx$ is...