integrals

[man111]

[tex](1)\;\; \int_{0}^{\infty}\frac{\sin x}{x+\mid \sin x\mid}dx[/tex]

[tex](2)\;\; \int_{0}^{1}\frac{(x-1)^2.(\cos x+1)-(2x-1).\sin x}{(x-1+\sqrt{\sin x})^2}dx[/tex]

[tex](3)\;\;\int_{\frac{\pi}{6}}^{\frac{\pi}{3}}\frac{1}{\sin^2 x.\sin^2(x+\frac{\pi}{6})}dx[/tex]

[tex](4)\;\; \int\frac{x^2+\cos^2 x}{1+x^2}dx[/tex]