Integration by recognition is what my textbook calls it. IMO it (can be/is) the hardest thing on the course.

It is probably one of the easiest things to do. There is no thinking required, just follow the steps that VCAA hand out for you. It's also a matter of setting out your notation well:

Example

a. Find the derivative of xlogx with respect to x.

d[xlogx]/dx = (1)*logx + x*(1/x) = logx + 1

(I strongly recommend this notation because it will be clear how to proceed in the next step)

b. Hence, find the antiderivative of logx.

Integrate both sides with respect to x:

=> xlogx = INTEGRATE[logx] + x

=> INTEGRATE[logx] = xlogx - x

(The anti-derivative cancels out with the derivative)

That's what you yield algebraically. You should however, note that there is a constant of integration within that integral. Your general solution would be:

INTEGRATE[logx] = xlogx - x + C

edited to correct for a stupid mistake; thanks Ahmad