When I try to integrate by parts, I end up in an infinite loop. Why is this, and how do you stop?

This could be happening for two reasons.  

Firstly, the negative form of the expression that you are being asked to integrate could be appearing in your answer, after you've used the 'integrating by parts' method once. If you try and integrate THAT, you'll end up where you started.  The way to solve this: Add the repeated integral to both sides. You'll be left with a definite integral which you can evaluate, then, when you divide both sides by two, you'll have the correct answer!

//The other reason it could be doing this is if you are using Integration by Parts twice in succession, and not being //consistent with your method. Eg, the integral of xIf for the first time you diff