Using Extended Euclidean Algorithm find the multiplicative inverse of $x^2+1$mod$(x^3+x+1).$ Once identified, express the multiplicative inverse polynomial as an integer in base $10.$

$\backslash$table$[[q,a,$b$,$r$,t_1,t_2,],[,x^3+x+1,x^2+1,,0,1,],[,,,,,,],[,,,,,,]]$