Match the following

A-S,B-R,C-Q,D-P
A) $$\begin{gathered} 2{\int }_0^{\frac{\mathrm{\pi }}{2}} \frac{1}{4-{\sin }^2\mathrm{x}}\mathrm{dx};2{\int }_0^{\frac{\mathrm{\pi }}{2}} \frac{{\sec }^2\mathrm{x}}{4+3{\tan }^2\mathrm{x}}\mathrm{dx}\tan \mathrm{x}=\mathrm{t} \\ 2{\int }_0^{\mathrm{\infty }} \frac{\mathrm{dt}}{4+(\sqrt{3}\mathrm{t}{)}^2}=2\cdot \frac{1}{2\sqrt{3}}{\left({\tan }^{-1}\frac{\sqrt{3}\mathrm{t}}{2}\right)}_0^{\mathrm{\infty }};\frac{\mathrm{\pi }}{2\sqrt{3}} \end{gathered}$$
B) $$\begin{gathered} I{\int }_0^{\pi } \frac{x}{4-si{n}^{2}x}dx;2I=\pi {\int }_0^{\pi } \frac{dx}{4-si{n}^{2}x}=\frac{{\pi }^2}{2\sqrt{3}} \\ I=\frac{{\pi }^2}{4\sqrt{3}} \end{gathered}$$
C) $$\begin{gathered} \mathrm{I}=2{\int }_0^{\frac{\mathrm{\pi }}{2}} \frac{\sin \mathrm{x}}{4-{\sin }^2\mathrm{x}}\mathrm{dx}={\int }_0^{\frac{\mathrm{\pi }}{2}} \left(\frac{1}{2-\sin \mathrm{x}}-\frac{1}{2+\sin \mathrm{x}}\right)\mathrm{dx} \\ =\frac{\mathrm{\pi }}{3\sqrt{3}} \end{gathered}$$
D) $2\mathrm{I}=\mathrm{\pi }{\int }_0^{\mathrm{\pi }} \frac{\mathrm{xsin}\mathrm{x}}{4-{\sin }^2\mathrm{x}}=\frac{{\mathrm{\pi }}^2}{3\sqrt{3}}$