Calculus

Hi. How can I integrate 1/(X^3 +1) ? Thank you to anyone who can help me :-)

Write 1/(x^3 +1) as
1/[(x+1)(x^2-x+1)]
Then use integration by parts, letting
dv = dx/(x^2 -x +1)
u = 1/(x+1)
du = log (x+1)
v = (2/sqrt3)arctan[(2x-1)/sqrt3]

That should take you to the answer. I know what the answer is (from my table of integrals), but have not done all the steps.

Could you by any chance tell me what your table of integrals says. I can't find it on mine to check my answer

OK. The answer is
(1/3){(1/2)log[(x+1)^2/(x^2-x+1)] + sqrt3*arctan[(2x-1)/sqrt3]}

Quite a mess. My approach does seem to lead to that answer.

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