Evaluate $\int\frac{dx}{x^3+1}$ without using partial Fractions Evaluate $$I=\int\frac{dx}{x^3+1}$$ without using partial Fractions
I tried in this way: 
$$I=\int \frac{\frac{xdx}{x^4}}{1+\frac{1}{x^3}}$$
Put $1+\frac{1}{x^3}=t$
$$I=\frac{-1}{3}\int \frac{dt}{t(t-1)^{\frac{1}{3}}}$$
Any way to help me?

hint
Write the integrand as
$$\frac {1}{x^3+1}=1-\frac {x}{3}\frac{3x^2}{x^3+1}$$
and integrate by parts.
