If f(x)=∑n=0∞xnf(x) = \sum_{n=0}^{\infty} x^nf(x)=∑n=0∞xn for ∣x∣<1|x| < 1∣x∣<1, find ∫0xf(t) dt\int_0^x f(t) \, dt∫0xf(t)dt.
∑n=0∞xn+1n+1\sum_{n=0}^{\infty} \frac{x^{n+1}}{n+1}∑n=0∞n+1xn+1
∑n=0∞xn+1\sum_{n=0}^{\infty} x^{n+1}∑n=0∞xn+1
∑n=1∞xnn\sum_{n=1}^{\infty} \frac{x^n}{n}∑n=1∞nxn
Both (a) and (c)