Identify the Maclaurin series for f(x)=∫0xcos(t2)dtf(x) = \int_0^x \cos(t^2) dtf(x)=∫0xcos(t2)dt.
∑n=0∞(−1)nx4n+1(4n+1)(2n)!\sum_{n=0}^{\infty} (-1)^n \frac{x^{4n+1}}{(4n+1)(2n)!}∑n=0∞(−1)n(4n+1)(2n)!x4n+1
∑n=0∞(−1)nx4n+1(2n+1)!\sum_{n=0}^{\infty} (-1)^n \frac{x^{4n+1}}{(2n+1)!}∑n=0∞(−1)n(2n+1)!x4n+1
∑n=0∞(−1)nx4n(4n)(2n)!\sum_{n=0}^{\infty} (-1)^n \frac{x^{4n}}{(4n)(2n)!}∑n=0∞(−1)n(4n)(2n)!x4n
∑n=0∞(−1)nx2n+1(2n+1)!\sum_{n=0}^{\infty} (-1)^n \frac{x^{2n+1}}{(2n+1)!}∑n=0∞(−1)n(2n+1)!x2n+1