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At first, you might think that it is possible to perform this integral simply by inspection, using the 'backwards chain rule'. This method would consist of adding one to the power, to get cos³(...

The standard rule for integration is: integrate kx^n dx = kx^(n+1)/(n+1). However, if we try and integrate 1/x in this manner we get, x^0/0, i.e. 1/0, which is infinity. However, if we look at a graph of ...

We recognise that this is in the form of a function within a function, i.e u= 3x - 2 is within the u^4 function, therefore here we will use the chan rule to differentiate the equation. 

T...

This is obviously a very important but somewhat difficult to explain question of maths. Let's try to define these terms for normal functions between R (real numbers) and R. 
Now, if we consider the d...

Integration by parts is used to integrate a product of functions. The formula is as follows:

Int[f(x)g'(x)] = f(x)g(x) - Int [f'(x)g(x)]