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apply power series methods here and find
use this integral to find a power series
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use this integral to find a power series
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use this integral to find a power series
for the natural log
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for the natural log
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for the natural log
and I'll do it by plugging in to this
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and I'll do it by plugging in to this
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and I'll do it by plugging in to this
expression what the power series for 1
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expression what the power series for 1
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expression what the power series for 1
over 1 plus T was and I know what that
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over 1 plus T was and I know what that
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over 1 plus T was and I know what that
is because I wrote it down on the board
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is because I wrote it down on the board
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is because I wrote it down on the board
up here change the variable from X 2 T
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up here change the variable from X 2 T
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up here change the variable from X 2 T
there and so 1 over 1 plus T is 1 minus
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there and so 1 over 1 plus T is 1 minus
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there and so 1 over 1 plus T is 1 minus
T plus T squared minus T cubed and so on
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so that's the thing in the inside of the
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so that's the thing in the inside of the
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so that's the thing in the inside of the
integral and now
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integral and now
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integral and now
it's legal to integrate that term by
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it's legal to integrate that term by
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it's legal to integrate that term by
term so let's do that
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