a way to integrate: $\int (\sqrt{x} +3)/(2+ x^ \frac{1}{3}) dx$ Im looking for a way to integrate: 
$$
\int \frac{ \sqrt{x} +3}{2+ x^ \frac{1}{3}} dx
$$ 
that would make it efficient and not too difficult...
Any suggestions? 

The substitution $x = t^6$ works. The integral becomes
$$ \int \frac{t^3 + 3}{t^2 + 2} \,6t^5\,dt = 6 \int \frac{t^8 + 3t^5}{t^2 + 2} dt = 6\int \left( t^6 - 2t^4 + 3t^3 + 4t^2 - 6t - 8 + \frac{12t+16}{t^2+2} \right) \, dt $$
You can take it from here
