Evaluate the indefinite integral as a power series $$\int \arctan (x^2)\, dx.$$ Find the first five non-zero terms of power series representation centered at $x = 0.$

---

Answer: $f(x) =$ $+$ $+$ $+$ $+$ $+ \cdots$

---

What is the radius of convergence?
Answer: $R =$

---

Note: Remember to include a constant "C".

---