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In the exam you will be given a fraction with polynomial numerator and denominator, the denominator will either be factored or factorable. Firstly, you need to factorize the denominator. Then to write as ...

The trick to solving this is to use the trig identity sin(a+b) = sin(a)cos(b) + sin(b)cos(a) From the identity above, we can write rewrite Rsin(x+c) as follows: Rsin(x+c)...

This can be done 'by parts' or by expanding. In this case it would be easier to expand as it is possible to deal with terms individually here.
This becomes: 10xx^1/2 - 10x2
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To solve the equation given in the question, we must first express the given equation in terms of only one trigonometric function, i.e. either all in cosec or all in cot. The easiest route would be cosec,...

Integrating by parts is simple. Simply put the equation into two parts, U and dV/dx. When considering which part of the original function will be U and which part will take dV/dx, you should consider whic...