Integrate the Maclaurin series for cos(x)\cos(x)cos(x) to find ∫cos(x) dx\int \cos(x)\,dx∫cos(x)dx.
∑n=0∞(−1)nx2n+1(2n+1)!+C\sum_{n=0}^{\infty} \frac{(-1)^n x^{2n+1}}{(2n+1)!} + C∑n=0∞(2n+1)!(−1)nx2n+1+C
∑n=0∞(−1)nx2n(2n)!+C\sum_{n=0}^{\infty} \frac{(-1)^n x^{2n}}{(2n)!} + C∑n=0∞(2n)!(−1)nx2n+C
∑n=1∞(−1)nx2nn+C\sum_{n=1}^{\infty} \frac{(-1)^n x^{2n}}{n} + C∑n=1∞n(−1)nx2n+C
∑n=0∞(−1)nx2n+2(2n+2)!+C\sum_{n=0}^{\infty} \frac{(-1)^n x^{2n+2}}{(2n+2)!} + C∑n=0∞(2n+2)!(−1)nx2n+2+C