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

Hi everyone, here is a new partial fractions question I just cannot understand:

[tex]\int[/tex][tex]\frac{x^{3}}{x^{3}+1}[/tex]dx

2. Relevant equations

Partial Fractions, difference of perfect cubes, polynomial long division

3. The attempt at a solution

[tex]\int[/tex][tex]\frac{x^{3}}{x^{3}+1}[/tex] dx

[tex]\int[/tex]1 dx + [tex]\int[/tex][tex]\frac{-1}{x^{3}+1}[/tex] dx

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

[tex]\frac{A}{x+1}[/tex] + [tex]\frac{B}{(x^{2}-x+1)}[/tex]

A(x[tex]^{2}[/tex]-x+1) + B(x+1) = - 1

If I use coefficients:

x[tex]^{2}[/tex]: 0=A

x: 0 = B-A

: -1 = A+B

These don't add up! Also, using critical values leads me to a similar problem. What am I doing wrong in my strategy of attacking these partial fractions??

Thank you for your time and help, you all are so wonderful!

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# Homework Help: Calc II - Integration of Partial Fractions

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