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

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Solution

$I = \int \frac{x^{2}}{x^{3} + 1} d x$ let $x^{3} + 1 = t$
$\Rightarrow 3 x^{2} d x = d t$
$\Rightarrow I = \frac{1}{3} \int \frac{d t}{t} = \frac{1}{3} l n t + C = \frac{1}{3} l n | x^{3} + 1 | + C$ .

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