How can I efficiently test for convergence in integrals without wasting time?

[MozAngeles]

Homework Statement

Hi, So i don't know if this is a stupid question but i'll ask anyways. So I'm on the chapter where we start testing integrals for convergence. The books starts out with elementary functions then they move towards non elementary functions. Testing for them is OK, my problem is that I cannot tell straight off the bat whether the integral is elementary, i waste a lot of time starting out trying to integrate. So is there any advice someone can give me that can help me identify my problem before i waste all the time?

Homework Equations

The Attempt at a Solution

 

[Dick]

If you can't integrate a function after a few tries, start thinking it's maybe not elementary and try to find a comparison test with something that is. In fact, even if a function IS elementary, if you only have to show convergence or divergence it's often easier to prove that by comparison with functions that are easier to integrate than to do the original integral.

 

[MozAngeles]

thanks. i realized after all these hours of studyin'