Mr. Integral
Math notes/Calculus II/Power Series and Taylor Approximation

Differentiating and Integrating Power Series — Cheat sheet

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Core rule

Differentiate or integrate power series term by term for ∣x−c∣<R|x-c|<R. The radius stays the same; endpoints may change.

Watch for

Track indices and integration constants. Substitution can change the radius in the new variable.