<s>[INST] Integration problem $\displaystyle \int \frac{dx}{x(x^3+8)}$ $$\int \frac{dx}{x(x^3+8)}$$
I think I'm supposed to use partial fractions, but I am unsure of how to start the problem. Any help would be appreciated. 
 [/INST] note that
$$x^5-32 = (x+2)(x^4-2x^3+4x^2-8x+16)$$
$$x^7-128 = (x+2)(x^6-2x^5+4x^4-8x^3+16x^2-32x+64)$$
$$x^9-512 = (x+2)(x^8-2x^7+4x^6-8x^5+16x^4-32x^3+64x^2-128x+256)$$
do you see the pattern?
now apply to pattern to
$$x^3+8$$
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