Question: Integrate the Taylor series for ex term by term, and find the value of the constant for which the integral matches the function ex. When

Integrate the Taylor series for ex term by term, and find the value of the constant for which the integral matches the function ex.
When a function has a well-behaved Taylor series, we can find a Taylor series for some integrals by integrating term by term (proving that these integrals converge to the correct answer requires methods from more advanced courses).

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