If $ƒ\left(\mathrm{x}\right)=\frac{\mathrm{x}+2}{2\mathrm{x}+3}$ . Then $\int {\left(\frac{\mathrm{ƒ}\left(\mathrm{x}\right)}{{\mathrm{x}}^2}\right)}^{1/2}\mathrm{d}\mathrm{x}$ is equal to

$\frac{1}{\sqrt{2}}\mathrm{g}\mathrm{ }\left(\frac{1+\sqrt{2\mathrm{ƒ}\left(\mathrm{x}\right)}}{1-\sqrt{2\mathrm{ƒ}\left(\mathrm{x}\right)}}\right)-\sqrt{\frac{2}{3}}\mathrm{h}\left(\frac{\sqrt{3\mathrm{ƒ}\left(\mathrm{x}\right)}+\sqrt{2}}{\sqrt{3\mathrm{ƒ}\left(\mathrm{x}\right)-\sqrt{2}}}\right)+\mathrm{ }\mathrm{c}$ where -

The integral$\int \frac{(2\mathrm{sin\theta }-1)\mathrm{cos\theta }}{5-{\cos }^2\mathrm{\theta }-4\mathrm{sin\theta }}d\theta$  is equal to

(where $C$ is a constant of integration)

Evaluate the following integral:

$\int \frac{xdx}{(x-1{)}^2(x+2)}$