What's the best integration technique to use amongst these (Intergration by parts, triginometric substitution, integrating rational fuctions b partial fractions)... and can you explain for what kind of integrands the technique works.

Question

What's the best integration technique to use amongst these (Intergration by parts, triginometric substitution,  integrating rational fuctions b partial fractions)... and can you explain for what kind of integrands the technique works.

anonymous · Answer

It all depends. Each technique has a different approach. I always start with "u substitution" and then move on. Normally the function will have a hint. By parts is functions that can't be integrated the other ways. An example would be like x^(2)sin(x). Trig substitution will have a square root in it and follow a general form. Partial fractions is used for rational functions when it would be easier to solve. I seem to try and for-see the what would happen if I did this...

anonymous · Answer

In my opinion there's no such thing as the "best" integration technique.  Integration proficiency only comes with lots of practice.

anonymous · Answer

Morales is right. There can be a better way to do a problem, but practice is golden.