General Discussion » Favorite integration techniques

When it comes to taking an antiderivative I find myself using parts a lot, but then I just look to my tables and realize I just wasted ten minutes with this function whos integral is neatly spelled out in the back of one of my cal books. Maybe I should study my tables more? Also, I like partial fractions, but I don't often need to use it.
What are your favorite integration techniques?

I fancy the integration by trigonometric substitution and the reduction formula.

Oh yeah, trig substitions come in handy, they can really turn a problem around, and the coolest thing is, once you get better with trig and are able to work with more identities, you can use them to do more trig substitutions, so its like you have more special moves! I need to go practice reduction....

I created an account just to reply:

Dude, find the technique that works best for your problem, and use it. Techniques of integration aren't an end in themselves, just a means to another end.

Realistically, we only teach integration techniques to help students work on their logical thinking skills. In the end, you should use the CAS of your choice to solve integrals and work on more interesting problems instead.

More interesting problems huh? There are always those interesting problems that I want to try...

A few come to mind...

http://en.wikipedia.org/wiki/Information_retrieval
http://en.wikipedia.org/wiki/Collaborative_filtering
http://en.wikipedia.org/wiki/Recommendation_system

:P