Starting from the power series $\ln(1+x) = \sum_{n=1}^{\infty} \frac{(-1)^{n-1}}{n} x^n$ for $|x| < 1$, find a power series representation for the following indefinite integral: $\int x \ln(1+x^2) dx$ centred at $a = 0$. What is the radius of convergence? (Note: Your answer for the integral should have a constant of integration $C$ in it.)
