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.

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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.

Mathematics
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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...
In my opinion there's no such thing as the "best" integration technique. Integration proficiency only comes with lots of practice.
Morales is right. There can be a better way to do a problem, but practice is golden.

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