Find the integral ∫∑n=0∞xndx\int \sum_{n=0}^{\infty} x^n dx∫∑n=0∞xndx within the radius of convergence.
∑n=0∞xn+1n+1+C\sum_{n=0}^{\infty} \frac{x^{n+1}}{n+1} + C∑n=0∞n+1xn+1+C
∑n=0∞xnn+C\sum_{n=0}^{\infty} \frac{x^n}{n} + C∑n=0∞nxn+C
∑n=0∞(n+1)xn+1+C\sum_{n=0}^{\infty} (n+1)x^{n+1} + C∑n=0∞(n+1)xn+1+C
∑n=0∞xn+1+C\sum_{n=0}^{\infty} x^{n+1} + C∑n=0∞xn+1+C