STEP I 1997 question 6 solution

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. The easiest way of doing the next bit would probably be long division, but that will be painful to layout in TeX. So, let's compare coefficients...

Coeff of

Coeff of

Coeff of

Coeff of

Coeff of

Coeff of

Coeff of

Coeff of (Which we knew it should be, but it never hurts to check).

Coeff of

Using this in the integral we get:

RHS = as required.

But and so .

So since we know we deduce .

Solution by DFranklin