# How to solve this integral $\int \frac{1+2x^2}{x^2(1+x^2)}dx$

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.

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 $x^2$
$\dfrac{1+2x^2}{x^2(1+x^2)}=\dfrac{1}{1+x^2}+\dfrac{1}{x^2}$