If the function $f(x) = \int \frac{x + 3}{x^2 - 9x + 20} dx$, then $f(x)$ is

For what values of $K$ is the function $f(x) = Kx^3 + 9x^2 + 9x + 3$ an increasing function on $R$?

Let $f(x) = \sin x$ and $g(x) = x$.
Statement-$1$: For $x \in (0, \infty)$,$f(x) \leq g(x)$.
Statement-$2$: For $x \in (0, \infty)$,$f(x) \leq 1$ but as $x \rightarrow \infty$,$g(x) \rightarrow \infty$.

The interval containing all the real values of $x$ such that the real-valued function $f(x) = \sqrt{x} + \frac{1}{\sqrt{x}}$ is strictly increasing is

If the maximum value of $a$,for which the function $f_{a}(x)=\tan ^{-1} 2 x-3 a x+7$ is non-decreasing in $\left(-\frac{\pi}{6}, \frac{\pi}{6}\right)$,is $\bar{a}$,then $f_{\bar{a}}\left(\frac{\pi}{8}\right)$ is equal to

If $f(x) = x^3 + bx^2 + cx + d$ and $0 < b^2 < c$,then on $R$,$f(x)$ is: