Re: [MLUG - DISCUSSION] Yet Another Wacky Integral...

[Stephen Montgomery-Smith <EMAIL:PROTECTED>]

Jonathan King wrote:
> 
> OK, so we need to solve the following integral:
> 
>    \int_0^z\frac{dx}{(1+x)^2(1+ax)}
> 
> No money involved; just your Geek Pride. :-)

Partial fractions are your friend - in Mathematica the command
Apart[1/((1 + x)^2(1 + a x))]

1/((1 - a)*(1 + x)^2) 
  - a/((-1 + a)^2*(1 + x))
  + a^2/((-1 + a)^2*(1 + a*x))

(but it would be quite easy to do by hand).

So the indefinite integral evaluates to:

1/((-1 + a)*(1 + x)) - (a*Log[1 + x])/(-1 + a)^2 + 
  (a*Log[1 + a*x])/(-1 + a)^2

Mathematica and Maple are both available for Linux, and MU has a site
license, so faculty can use it for about $25 per computer per year.  The
Maple license even allows faculty to use Maple on their home computers
for the same fee.

> pps--Thanks ahead of time to Stephen Montgomery-Smith. :-)
>      --Jeff Rouder and Jon King

Best to also email me directly because I don't always follow mlug.

-- 
Stephen Montgomery-Smith
EMAIL:PROTECTED
http://www.math.missouri.edu/~stephen
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