I am trying to integrate x^2/(1+x^2 ) from 0 to 1.
The Attempt at a Solution
We recently worked on trig substitutions in class, but, rather than substituting x for tan(theta) I think there may be an easier way via algebraic manipulation. If I divide both numerator and denominator by the highest power of X in the denominator (x^2), then I get back out
which is equal to x^2/2.
Now, I can easily integrate 1/2 x^2 without trig substitution.
My main question is: Is this a viable method for simplifying the integral, or must I go through trig substitution?