Evaluate:
$\int \frac{x^{2}}{1 + x^{3}} d x$

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Solution

$\begin{matrix} Let 1 + x^{3} = z \Rightarrow 3 x^{2} d x = d z \Rightarrow x^{2} d x = \frac{d z}{3} ∴ \int \frac{x^{2}}{1 + x^{3}} d x = \frac{1}{3} \int \frac{d z}{z} = \frac{1}{3} log | z | + C = \frac{1}{3} log ∣ ∣ 1 + x^{3} ∣ ∣ + C \end{matrix}$

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