Additional Mathematics - Integration

Integration is the reverse process of differentiation.
For eg,
when we differentiate 'A', we get 'B'.
when we integrate 'B', we get 'A'

To solve integration problems, we need a copy of the formulaes with us. I find the integration formulae list in the Longman A Maths guide comprehensive.

But there are some integration questions that I am unable to solve, even with the formulae.
For eg, Integrate (x)/[sq root(x - 1)].
The answer is y = (x + 2)[sq root(x - 1)]
I know the answer because this is a guided question.
Part 1 of the question requires me to differentiate y = (x + 2)[sq root(x - 1)]. The answer is (3/2)(x)/[sq root(x - 1)]
And Part 2 of the question requires me to integrate (x)/[sq root(x - 1)], which is the original function y.

Thankfully, I have not come across a question in the past 10 years of Additional Mathematics GCE 'O' level examination that requires integration of a complicated function without providing any guides. ^o^

In the integration formulaes provided, integrate (1/x) is (ln x + C). But, it does not say what is the answer for integrating (ln x). Luckily, I found an answer through a guided question. And, I thought I should record in this space for my readers.

Integrate (ln x) = (x)(ln x) - x + C
Integrate (x)(ln x) = (1/2)(x2)(ln x) - (1/4)(x2) + C
Integrate (x2)(ln x) = (1/3)(x3)(ln x) - (1/9)(x3) + C
follow the pattern.

Happy Integration ^o^