How do you show whether the improper integral #int dx / (x^2 + sinx)# converges or diverges from 2 to infinity?

Related questions

• What is the Integral Test for Convergence of an Infinite Series?
• How do you know when to use the integral test for an infinite series?
• How do you use the Integral test on the infinite series #sum_(n=1)^oo1/root5(n)# ?
• How do you use the Integral test on the infinite series #sum_(n=1)^oo1/n^5# ?
• How do you use the Integral test on the infinite series #sum_(n=1)^oo1/(2n+1)^3# ?
• How do you use the Integral test on the infinite series #sum_(n=1)^oo1/sqrt(n+4)# ?
• How do you determine if the series #ln(1/2) + ln(1/3) + ln(3/4) + ... +ln[k/(k + 1)] + ....# converges?
• How do you know #{-1,1,-1,1,-1,1,...}# converges or diverges?
• Using the integral test, how do you show whether # (1 + (1/x))^x# diverges or converges?
• Using the integral test, how do you show whether #sum 1/(n^2+1)# diverges or converges from n=1...