$\int_2^4 \frac{\log x^2}{\log x^2+\log \left(36-12 x+x^2\right)} \mathrm{d} x$ is equal to

The value of $\int_0^2\left[x^2\right] \mathrm{d} x$ is (where $[x]$ denotes the greatest integer function not greater than $x$ )

$$ \int_0^3 \frac{d x}{(x+2) \sqrt{x+1}}= $$

$$ \int_0^{\frac{\pi}{2}} \frac{d x}{1+(\cot x)^{101}}= $$