Choosing the correct method of integration.

[eliwood1221]

Hey, i am just wondering how one chooses whether the proper method for integration is by parts, or by substitution. if by some OBSCURE method of substitution gives me the correct answer, will integrating by parts give the same? for example
INTEGRAL 2t/((t-3)^2) dt. i used a parts substitution first, and got one answer, but it is different than other answers generated by substitution..

 

[nicksauce]

If you integrate correctly, no matter the method of integration, then your answer will always be the same, up to a constant. Perhaps you can show your work so we can try to figure out where you may have gone wrong?

 

[Integral]

The preferred method is the easiest one that gets the job done. It does not matter what method you use, if applied properly the result will be the same. If you do not get the same result with different methods you have made an error in one or the other. You also might want to check that your results are just different expressions of the same thing.