How Can the Integral Be Simplified for Easier Evaluation?

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The integral A = ∫01 (4x + 3) / (x2 - x + 1)2 dx can be simplified by expressing the numerator in relation to the denominator. By rewriting the numerator as a linear combination of the derivative of the denominator and a constant, the evaluation of the integral becomes more straightforward. This approach leverages integration techniques such as substitution and partial fractions for efficient computation.

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Evaluate

[tex]A \ = \ \int_{0}^{1} \frac{ 4x \ + \ 3 }{ ( x^2 - x +1 )^{2} } dx[/tex]
 
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Express the numerator in such terms that it has some relation to the denominator plus some constants.
 

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