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I'm pretty new to calculus, but is there a way to reverse the chain rule so I can take the antiderivative of 1/(x^3+1) without using partial fractions?

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Reversing the Chain Rule when finding an antiderivative is Integration by Substitution. You will use it during the integration.

But the partial fractions decomposition comes first.

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The partial fractions answer is worked out here.

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    $\begingroup$ Actually, reversing the chain rule is more like $u$-substitution. $\endgroup$
    – JimmyK4542
    Aug 23, 2014 at 5:06
  • $\begingroup$ Oh I was thinking product rule for some reason. $\endgroup$
    – user109775
    Aug 23, 2014 at 5:11

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