Evaluate ∫01sinxxdx\int_0^1 \frac{\sin x}{x} dx∫01xsinxdx as an infinite series.
∑n=0∞(−1)n(2n+1)(2n+1)!\sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)(2n+1)!}∑n=0∞(2n+1)(2n+1)!(−1)n
∑n=0∞(−1)n(2n+1)!\sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)!}∑n=0∞(2n+1)!(−1)n
∑n=0∞(−1)nn(2n+1)!\sum_{n=0}^{\infty} \frac{(-1)^n}{n(2n+1)!}∑n=0∞n(2n+1)!(−1)n
∑n=0∞(−1)n(2n+2)!\sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+2)!}∑n=0∞(2n+2)!(−1)n