The value of the integral $\int_{\frac{-\pi}{2}}^{\frac{\pi}{2}}\left(x^2+\log \frac{\pi-x}{\pi+x}\right) \cos x d x$ is equal to

For the system $x-y+z=4,2 x+y-3 z=0$, $x+y+z=2$, the values of $x, y, z$ respectively are given by

The value of $\int \sin \sqrt{x} \mathrm{dx}$ is equal to

If the vectors $\overline{A B}=3 \hat{i}+4 \hat{k}$ and $\overline{A C}=5 \hat{i}-2 \hat{j}+4 \hat{k}$ are the sides of the triangle $A B C$, then the length of the median through $A$ is