Integrate 1/(x^2-x+a) from 0 to 1/2 using power series

huntsiekfind

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May 22, 2009
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7
I am totally lost on this one, can you please help me.

By factoring x^3 +1 as a sum of cubes, rewrite

1/2
?dx/x^2-x+1=?/3?3
0

Then express 1/x^3+1 as the sum of a power series and use it to prove the following formula for ?

?
?=3?3/4?(-1)^n/8^n[(2/3n+1) + (1/3n+2)]
N=0
 
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