I will say that this was a particularly nasty question… the fact that it is an integral on top of the fact that we can’t easily use the ‘cheat’:

… and I suppose no help with the factorisation also

The following should answer your question:

Your partial fraction expansion is correct and the integral is equal to:

.

The first anti-derivative is easy because it is a : the -substitution will yield:

.

The second term is more troublesome. The marking scheme does the substitution… here I show how to do what you are trying to do properly…

Taking

.

This is not equal to

.

Looking at :

.

Therefore we can say

via the ‘cheat’.

I hope this answers your question. Your question won’t be an integral.

Regards,

J.P.

Need some help with Winter 2014 Q. 3(a) iii.

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