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    Hi I was just wondering what is the order of preference for the choice of u in by parts ?

    ln
    polynomial ...

    is this right? + what else eg trig?
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    You just need practice; if you choose them the wrong way round you'll get uv - integral of something which requires integration by parts again. The best way is to try and see if it works, and if not try again. Other times you WILL have to use integration by parts twice, because both ways will give you a second integral requiring it. With lnx you'll have to take it as u.
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    Most people just recognise it from practice. However, you could memorise logarithmic functions, inverse trig functions (e.g; arctan), power functions ( e.g; x squared), trig functions, then exponential functions. But it is best to understand why it this order (e.g; log functions can easily be differentiated, but there is not a standard antiderivative for the natural log).
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    The one that simplifies the most when you differentiate ideally so that you get an integer eg. X is better to be u than e^x as you want to end up with only one function to integrate otherwise you would have x^2 / 2 e^x however as well as this ln x and tan x must be chosen as u no matter what the other function is because they cannot be integrated.
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    thanks everyone
 
 
 
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