### Eric Nicholas K's answer to New Zealand's JC Malaysia question.

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There are three things that we need to do for substitutions.

1. DIfferentiate u with respect to x and obtain du in terms of dx

2. Express x in terms of u so that we can make later substitutions.

3. Change the limits of integration from x to u i.e. x to ln x.

Finally, we place everything in. Do everything at the same step i.e. change the limits and the letters all at once or there may be confusions.

Halfway through, I realise that I have to do integration by parts. You will then need to apply the idea for integration by parts which you probably know how to do.

Of course, since the letter u is being used here, calling out 'du/dx' does not make sense since u is the variable to be differentiated or integrated (and therefore du should be at the bottom of the fraction), hence I call the expression 'dp/du' and 'dq/du'.

1. DIfferentiate u with respect to x and obtain du in terms of dx

2. Express x in terms of u so that we can make later substitutions.

3. Change the limits of integration from x to u i.e. x to ln x.

Finally, we place everything in. Do everything at the same step i.e. change the limits and the letters all at once or there may be confusions.

Halfway through, I realise that I have to do integration by parts. You will then need to apply the idea for integration by parts which you probably know how to do.

Of course, since the letter u is being used here, calling out 'du/dx' does not make sense since u is the variable to be differentiated or integrated (and therefore du should be at the bottom of the fraction), hence I call the expression 'dp/du' and 'dq/du'.

Date Posted:
5 months ago