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Usually the easiest way to find the root of a quadratic is to factorise it so you have something a form similar to - (x+2)(x-1)=0. From here you need to find a value for x that makes each bracket equal to ze...

The integral of log(x) is not necessarily straight-forward. Though we can use the fact that d/dx(log(x)) = 1/x to help us. Rather than simply trying to integrate log(x), we can use integration by parts on 1 ...

The key to solving any integral of this form is to use the cosine rule: cos(2x) = cos 2 (x) - sin 2 (x) = 2 cos 2 (x) - 1 = 1 - 2 sin 2 (x) All of these forms are really helpful when solving problems such as...

y=x^ x To find the differential, dy/dx, logs of both sides must be taken: log(y)=log(x^ x ) Then using log rules, the power can be brought down, outside the log expression: log(y) = x log(x) This expre ssion...

If you aren't lucky enough to be told in the question, the first thing we have to do is know when we should you integration by parts. Well, like most things in maths this should become second nature to you w...