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What we should know is that the root 3+4i is a complex number that looks alot like a+bi.

We can say : rt(3+4i) = a+bi (Where we dont know what a & b is..yet)

and when we square both side...

Our given equation is d²x/dt² + 5dx/dt + 6x = 0, which we need to recognise as a second order differential equation. Therefore we need to begin by solving the auxilary funtion m^...

This is an example of an integral that uses trigonometric substitutions, which is quite a common theme for A-level further maths questions. Firstly, notice the denominator is quite unpleasant, so to make ...