Originally Posted by

**arbolis** I must solve $\displaystyle (1+x^2)y'+4xy=\frac{1}{(1+x^2)^2}$.

I think it's a first order linear non homogeneous DE which can be solved by the integrating factor method.

So far I've rewritten the equation as $\displaystyle \frac{dy}{dx}+ \underbrace {\left ( \frac{4x}{1+x^2}\right ) }_{p(x)} y=\underbrace{\frac{1}{(1+x^2)^3}}_{q(x)}$.

I found the integrating factor to be $\displaystyle 2 \ln (1+x^2)$.

So multiplying the DE by it and integrating with respect to x, I found out that $\displaystyle 2 \ln (1+x^2)=2 \int \frac{\ln (1+x^2)}{(1+x^2)^3}dx$.

I thought of using integration by parts to solve the integral, but I'm stuck at finding a primitive of $\displaystyle \ln (1+x^2)$, as stupid as it may sound.

Am I in the right direction? If so, could you provide a tip to find a primitive of $\displaystyle \ln (1+x^2)$?

Thanks in advance.