Question

integral t^2/(1+t^2)

Answer 1

Let's do a sneaky little math trick.\[\Large \int\limits \frac{t^2}{1+t^2}dt\quad=\quad \int\limits \frac{1+t^2-1}{1+t^2}\]\[\Large =\quad \int\limits \frac{1+t^2}{1+t^2}-\frac{1}{1+t^2}dt\quad=\quad \int\limits 1-\frac{1}{1+t^2}dt\]

Answer 2

If that process is too confusing, you can always do `Polynomial Long Division` since the degree of the numerator is equal to the degree of the denominator.