I don't really understand this at all. I think you have to use the derivative of $\cos(x^2)$ which is $-2x\sin(x^2)$, and use the power series of $\sin(x)$, but I don't know where I would go from there...
2026-03-25 04:58:48.1774414728
Using power series, find an indefinite integral of $f(x)=\cos(x^2)$.
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We know that:
$$cos(x^2)=\sum_{k=0}^\infty (-1)^k \frac{x^{4k}}{(2k)!}$$
Therefore,
$$\int cos(t^2)=\sum_{k=0}^\infty (-1)^k \frac{x^{4k+1}}{(4k+1)(2k)!}$$
There is no closed form of the expression of such an indefinite integral, it's a Fresnel integral if you want to know more about it.