Word Count : 200

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Let $I = \int \frac{x^2 \cot^{-1}(x^3)}{1 + x^6} \, dx$. Notice that $1 + x^6 = (1 + x^3)(1 - x^3 + x^6)$, but a better approach is substitution. Set $t = x^3 \implies dt = 3x^2 dx \implies x^2 dx = \frac{dt}{3}$. Then the integral becomes: $$ I = ____ ____ _________ ________ _______ _________ ___ ____.
___ ____ ___ ________ ______ ______.
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