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This equation has one function of x divided by another function of x, we therefore have to use the quotient rule and is written in the form f(x)/g(x). 

The quotient rule is therefore

We use parts for this integration even though there is only one term! make ln(x)=1ln(x)

How to do integration by parts

If you have a function that you need to integra...

Here, we must apply both chain and product rules. The chain rule can be used to find the derivative of a function in the form e^f(x), like this one. However it is useful to know that this will r...

This is one of the trickier methods of integration, and it requires some practise. The basic idea is to split a function which would be difficult to integrate into two parts. Differentiating one part a...

The first thing to recognise is that this function is a product of two functions: namely, 4x^2 and ln(x), thus we must employ the product rule in order to find the solution. As you may recall, the prod...