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psychopath
03-17-2009, 05:03 PM
Was studying for my calculus exam, and came across something in a solution I don't quite understand.

How does the integral of 2x^2/1+x^2 turn into 2*the integral of 1-(1/1+x^2) (integral bounds are 0 to 1).

I understand how the 2 moves out of the integral, but I don't know how it turns into 1-(1/...). Is it some sort of rule I missed?

brewbuck
03-17-2009, 05:13 PM
It is just algebra.

You can write 1 as (1+x^2)/(1+x^2). So:

1 - 1/(1+x^2) = (1+x^2)/(1+x^2) - 1/(1+x^2) = (1+x^2-1)/(1+x^2) = x^2/(1+x^2)