The improper integral $\backslash$int$\_1^$x $($cos$^(2)$x$)/(1+$x$^(2))$dx$,$ since,

A$.\backslash$int$\_1^(\backslash$infty $)($cos$^(2)$x$)/(1+$x$^(2))$dx$=\backslash$lim$\_($t$->\backslash$infty $)\backslash$int$\_1^$t $($cos$^(2)$x$)/(1+$x$^(2))$dx does not exist.

B$.($cos$^(2)$x$)/(1+$xx$^(2)+1)$ for x$>=1$ and $\backslash$int$\_1^(\backslash$infty $)(1)/($x$^(2)+1)$dx$=(\backslash$pi $)/(4).$

c$.(1)/($xcos$^(2)$x$)/(1+$x$^(2))$ for x$>=1$ and $\backslash$int$\_1^$x $(1)/($x$)$dx diverges.

D$.($cos$^(2)$x$)/(1+$xx$^(2))$ for x$>=1$ and $\backslash$int$\_1^(\backslash$infty $)(1)/($x$^(2))$dx converges.

Note: there may be more than one correct answer. Select all that apply.