Evaluate the indefinite integral as a power series?
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Question “Evaluate the indefinite integral as a power series?”
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Answer
Explanation:
For an example, consider the power series expansion
This is an important one to remember. However, it can be derived as follows:
Letting
Perform an index shift
This allows us to rewrite our given integral indefinitely as follows:
Multiply the
This series’ radius of convergence is
We do term-by-term Integration on the Series:
We are leaving
Still, the radius of convergence is
Conclusion
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