When integrating by parts, how do I decide which part of the integrand is u or f(x) and which dv or g'(x)?

Integration by parts is not only a very useful techinque for integrating, but it is also one of the techinques that appears more in the IB Mathematics exams. The most important step is to choose the part of the integrand that works better for u or f(x), as a right choice will save you a lot of time (and time is everything in the IB!). Whenever you are in doubt, choose u or f(x) to be the following:

1. The LOgarithm. If there is none,
2. The ROot. If there is none,
3. The POlynomial. If there is none,
4. The Trigonometric function. If there is none,
5. The Exponential function. To remember this rule, think about the sentence "LOve ROasted POtatoes Till the End", and its initials will tell you the order of the functions you need to look for to be u or f(x)!!