Integration of $\ln (x)$ with $x$ i.e.

$$ \int \ln (x) d x= $$__________

The function $f(x) = x^3 - 27x + 4$, $1 \leq x \leq 6$ has

The smallest positive root of the equation $$x^5 - 5 x^4 - 10 x^3 + 50 x^2 + 9 x - 45 = 0$$ lies in the range

For the integral $\rm I=\displaystyle\int^1_{-1}\frac{1}{x^2}dx$

which of the following statements is TRUE?