<s>[INST] Integrate $ \int \frac{1}{1 + x^3}dx $ $$ \int \frac{1}{1 + x^3}dx  $$
Attempt:
I added and subtracted $x^3$ in the numerator but after a little solving I can't get through.
 [/INST] You can factor the denominator using the formula $a^3+b^3=(a+b)(a^2-ab+b^2)$, and in our case $a=x$ and $b=1$
$$\int \dfrac{1}{(x+1)(x^2-x+1)} dx$$
Assume  $\dfrac{1}{(x+1)(x^2-x+1)} = \dfrac {A}{x+1} + \dfrac {Bx+C}{x^2-x+1} $
Can you take it from here?
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