Integrate $\int{\frac{1}{x\sqrt{1-x^3}}dx}$

Question

How do I integrate $$\int{\frac{1}{x\sqrt{1-x^3}}dx}$$

Not able to think of a method. Any hint is appreciated. Thanks

Answer 1

Hint:

Generalization:

$$\dfrac1{x\sqrt[n]{1-x^m}}=\dfrac{mx^{m-1}}{mx^m\sqrt[n]{1-x^m}}$$

Now choose $\sqrt[n]{1-x^m}=v\implies dv=?$

Answer 2

Hint : Substitute $u=\sqrt{1-x^3}$