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Now, can we do something else interesting with series? Let’s try integration. Let us look at

Integrating that gives us

The constant of integration has to be 0. We can find that by substituting *x* by 0.

Integrating again gives us

We get a constant of integration in the end, but that can easily be found to be 0.

The series for cos(*x*) can be found by differentiating the series for sin(*x*).

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