I want to solve the following IVP :
\begin{cases} u_{tt} - u_{xx} = 0 \; & \text{in} \; \mathbb{R} \times(0,+\infty) \\ u = \cos ^2 x, \; u_t = \ln^2 {(1+x^2)} \; & \text{on} \; \mathbb{R} \times\{t = 0\} \end{cases}
if I use D'Alembert's formula I'll have to find a primitive of $\ln^2 {(1+x^2)}$
which I tried computing using an integration by parts, so firstly I had to find $\int \ln (1+x^2)\, dx = x \ln (1+x^2) +2(\arctan x - x )$ and then I got stuck in on the integrals that's appeared which is $\int \frac{x \arctan x}{1+x^2}\, dx$ which by means of a u-substitution I could reduce to $\int u \tan u \, du$ but I couldn't go further.
any help will be greatly appreciated.