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Evaluate: int(x^2)/(1+x^3)\ dx...

Evaluate: `int(x^2)/(1+x^3)\ dx`

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Solution:
Let `I=\int \frac{x^{2} d x}{1+x^{3}}`
Putting `1+x^{3}=t`
`\Rightarrow 3 x^{2} \{dx}=d t`
`\Rightarrow x^{2} \{dx}=\frac{d t}{3}`
`\therefore I=\frac{1}{3} \int \frac{d t}{t}`
=`\frac{1}{3} \ln |t|+C`
=`\frac{1}{3} \ln 1+x^{3}+C\left(t=1+x^{3})`
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