(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[tex]\int\frac{4x^5-1}{(x^5+x+1)^2}dx[/tex]

2. Relevant equations

This is in the section on Partial Fractions. The main idea in this section was that you get the integral down to a sum integrals of the following forms:

[tex]\int\frac{dx}{(x+a)^n} , \int \frac{x dx}{(x^2 + bx + c)^m} , \int \frac{dx}{(x^2+bx+c)^m}[/tex]

3. The attempt at a solution

The basic approach for most of these was to just use partial fractions by factoring the denominator and algebraically breaking down the result. I factored the denominator to

[tex]\left(x^2+x+1\right)^2\left(x^3-x^2+1\right)^2[/tex]

The term on the right could be factored again, but it doesn't look promising.

I sense I should be using a different approach with this problem, but I'm not sure what.

Please just give me a hint, if possible.

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# Integrating (using partial fractions) Apostol Section 6.25 #25

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