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jbowers9
jbowers9 is offline
#3
Dec9-07, 12:21 PM
P: 70
I found the following link at math.com

http://www.math.com/tables/expansion/log.htm

I derived the first expression in the link and the one you gave the following way:

1/1-x = 1 + x + x^2 + x^3 + ...
let x = -x and integrate
1/1+x = 1 - x + x^2 - x^3
int {1/1+x dx} = x - x^2/2 + x^3/3 - x^4/4 ... = ln(1+x)
let x = x-1
ln(x) = (x-1) - (x-1)^2/2 + (x-1)^3/3 ... 0 < |x| < 1
The above expression is invalid at x=0.
How are the three expressions following the first in the link derived?