# Integrate the following using infinite #\bb\text(series)# ?

##
(a) #\int(\arctan(4x))/(x^-7)dx#

(a)

Start from:

Expand now the integrand using the geometric series:

and integrating again term by term:

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To integrate using an infinite series, follow these general steps:

- Express the function as a power series if possible.
- Determine the interval of convergence for the power series.
- Integrate the power series term by term within the interval of convergence.

If you have a specific function or expression you'd like to integrate using an infinite series, please provide that information so I can assist you further.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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