<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] partial fraction : in general form ,write it like below 
  and find  A,B,C 
$$\frac{x}{a+bx^3}= \\ \frac{x}{(\sqrt[3]{a}+\sqrt[3]{b}x)((\sqrt[3]{a})^2+(\sqrt[3]{b}x)^2-(\sqrt[3]{a}\sqrt[3]{b}x))}=\\ \space \\ \frac{A}{(\sqrt[3]{a}+\sqrt[3]{b}x)}+\frac{Bx+C}{((\sqrt[3]{a})^2+(\sqrt[3]{b}x)^2-(\sqrt[3]{a}\sqrt[3]{b}x))} $$ then you will have logarithm part  + log or arctan part (depends on a,b)
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