Let $f(x)$ be the differentiable function for all $x$ such that $f'(x) \leq 5$ and $f(1) = 4$. The maximum value of $f(5)$ is...

If $\int x^2 \cdot e^x dx = e^x f(x) + c$, then the minimum value of $f(x)$ is ...

$\int \dfrac{(x+1)}{x(1+xe^x)^2}dx =$

If $\int \dfrac{x+1}{x^2+1}dx = \tan^{-1}x + g(x) + c$, where $c$ is constant of integration, then the function $g(x)$ is monotonically increasing in the interval