Use integration to find ∫0x∑n=0∞(−1)nt2ndt\int_0^x \sum_{n=0}^{\infty} (-1)^n t^{2n} dt∫0x∑n=0∞(−1)nt2ndt.
∑n=0∞(−1)nx2n+12n+1\sum_{n=0}^{\infty} \frac{(-1)^n x^{2n+1}}{2n+1}∑n=0∞2n+1(−1)nx2n+1
arctan(x)\arctan(x)arctan(x)
tan−1(x)\tan^{-1}(x)tan−1(x)
∑n=1∞(−1)n−1x2n−12n−1\sum_{n=1}^{\infty} \frac{(-1)^{n-1} x^{2n-1}}{2n-1}∑n=1∞2n−1(−1)n−1x2n−1