Express ∫0xsin(t2) dt\int_0^x \sin(t^2) \, dt∫0xsin(t2)dt as a power series.
∑n=0∞(−1)nx4n+1(2n+1)!(4n+1)\sum_{n=0}^{\infty} \frac{(-1)^n x^{4n+1}}{(2n+1)!(4n+1)}∑n=0∞(2n+1)!(4n+1)(−1)nx4n+1
∑n=0∞(−1)nx4n+3(2n+1)!(4n+3)\sum_{n=0}^{\infty} \frac{(-1)^n x^{4n+3}}{(2n+1)!(4n+3)}∑n=0∞(2n+1)!(4n+3)(−1)nx4n+3
x−∑n=1∞(−1)nx4n+1(2n+1)!(4n+1)x - \sum_{n=1}^{\infty} \frac{(-1)^n x^{4n+1}}{(2n+1)!(4n+1)}x−∑n=1∞(2n+1)!(4n+1)(−1)nx4n+1
∑n=0∞(−1)nx2n+1(2n+1)!\sum_{n=0}^{\infty} \frac{(-1)^n x^{2n+1}}{(2n+1)!}∑n=0∞(2n+1)!(−1)nx2n+1