1. **Problem statement:** Evaluate the indefinite integral $$\int \frac{t}{1 - t^5} \, dt$$ as a power series and find the radius of convergence $R$. 2. **Recall the geometric series formula:** For $|x| < 1$, $$\frac{1}{1-x} = \sum_{n=0}^\infty x^n$$ 3. **Rewrite the integrand:** $$\frac{t}{1 - t^5} = t \cdot \frac{1}{1 - t^5} = t \sum_{n=0}^\infty (t^5)^n = \sum_{n=0}^\infty t^{5n+1}$$ 4. **Integrate term-by-term:** $$\int \frac{t}{1 - t^5} \, dt = \int \sum_{n=0}^\infty t^{5n+1} \, dt = \sum_{n=0}^\infty \int t^{5n+1} \, dt = \sum_{n=0}^\infty \frac{t^{5n+2}}{5n+2} + C$$ 5. **Final power series expression:** $$C + \sum_{n=0}^\infty \frac{t^{5n+2}}{5n+2}$$ 6. **Radius of convergence:** The original series $$\sum_{n=0}^\infty (t^5)^n$$ converges for $$|t^5| < 1 \Rightarrow |t| < 1$$ so the radius of convergence is $$R = 1$$.