test & some help needed on LaTex.

$\displaystyle \displaystyle \oint^\frac{\pi}{4}_1 (\dfrac {\sqrt{(\sin (x +60^\circ)} + (\cos^2x)} {\csc{{3}{\pi}}x}) \,d\vec{x} $

Just a random string of math. How do i make the integration sign bigger,write $\displaystyle \pi$ over a number eg. pi/4 ,input the degree sign and extend the square root sign(if possible)?

More random playing around, I wanted to see how complicated it can get.

$\displaystyle \begin{array}{rcl}

\displaystyle \Huge\Sigma\oint^\frac{\pi}{4}_1 (\dfrac {\sqrt{(\sin (x +60^\circ)} + (\cos^2x)} {\csc(\frac{\pi}{2}\dfrac{22342}{{1}{\frac{2}{3}}} )x}) \,d\vec{x} =\\ \dfrac{tan^5x}{cosxsinx} + C \end{array}$