<s>[INST] Evaluate the integral $\int \frac{x}{a+bx^3}\ dx$ How do I solve integral at this form
$\displaystyle\int \frac{x}{a+bx^3}\ dx$ ? 
 [/INST] $$
a+bx^3 = (\sqrt[3]a +x\sqrt[3]b)(\sqrt[3]a^2 - x\sqrt[3]a\sqrt[3]b + x^2\sqrt[3]b^2)
$$
So use partial fractions:
$$
\frac x {a+bx^3} = \frac C {\sqrt[3]a +x\sqrt[3]b} + \frac {Dx+E} {\sqrt[3]a^2 - x\sqrt[3]a\sqrt[3]b + x^2\sqrt[3]b^2}
$$
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