How to solve this integral

$$\int \frac{1+2x^2}{x^2(1+x^2)}dx$$

I thought it should be $ x + 3x^2$ in the numerator so that I will take $x+x^3 = u$ then taking derivative both sides and it comes; $1+3x^2$ so this is wrong.

Please suggest how to proceed.


Hint: write the numerator as $1+x^2 + x^2$ and write the whole expression as two fractions. One with numerator $1+x^2$ and the other one with $x^2$



Use partial fractions.



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