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

The function $f(x)=4 \sin ^3 x-6 \sin ^2 x+12 \sin x+100$ is strictly

Function $f(x) = \log_{10} \cos x$ is . . . . . . function in the interval $\left(0, \frac{\pi}{2}\right)$.

For which interval is the given function $f(x) = -2x^3 - 9x^2 - 12x + 1$ decreasing?

Let $f(x) = \frac{x}{\sqrt{a^2 + x^2}} - \frac{d - x}{\sqrt{b^2 + (d - x)^2}}$,$x \in R$,where $a, b$ and $d$ are non-zero real constants. Then:

Statement $-1:$ The function $f(x) = x^2(e^x + e^{-x})$ is increasing for all $x > 0.$
Statement $-2:$ The functions $g(x) = x^2e^x$ and $h(x) = x^2e^{-x}$ are increasing for all $x > 0$ and the sum of two increasing functions in any interval $(a, b)$ is an increasing function in $(a, b).$