(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

The solution is

[tex]- \frac{x}{x^5 + x + 1}[/tex]

3. The attempt at a solution

Other than getting lucky and noticing immediately that this could be the derivative of a fraction, I do not see an easy way to solve this. The partial fractions solution is long and involved. I am reviewing calculus material to study for the math GRE, so am trying to see if there is a more efficient way. Given the level of the other exercises in this book, I would be surprised if there were not. Help me see the light! Thanks :-)

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# Tricky rational function integral

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