<p>I feel like I have a good grasp on all the techniques- but I never know which one to use! I end up wasting a lot of time, doing u substitution when I ought to be integrating by parts, or trying to use logs when I should be doing implicit differentiation.....etc. Any suggestions?</p>
<p>Hm... for substitution v. integration by parts, I'd look for a u term (in integration by parts) that would easily be reduced to nothing. Just try to be as lazy (in this case, meaning efficient) as possible. Spend a little time looking for the shortest possible method.</p>
<p>Ok, if you can't find a u subst. that will work (like the du term has a term in it that isnt in the original integral) Then try by parts.</p>