<s>[INST] How to compute $\int{\frac{5x^3+8x^2+x+2}{x^2(2x^2+1)}} dx$? $$\int{\frac{5x^3+8x^2+x+2}{x^2(2x^2+1)}} dx$$
So ... how do I start? Numerator cant be factorized it seems, and this looks like a complicated expression ... 
I tried expanding the denominator to see if integration by substitution will work, but it didn't give any ideas
$$\int{\frac{5x^3+8x^2+x+2}{2x^4+x^2}} dx$$
I don't see a clear way to integrate by parts either. Can anyone enlighten me?
 [/INST] Hint :
Use partial fraction decomposition :
$$\frac{5x^3+8x^2+x+2}{x^2(2x^2+1)}=\frac{A}{x}+\frac{B}{x^2}+\frac{Cx+D}{2x^2+1}$$
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