# Math Help - confused-integration problem-URGENT

1. ## confused-integration problem-URGENT

$\int_0^2 \frac{(x+1)^2}{x^{2}+1} dx$

ok ive got to $\int_0^2 1.dx +\int_0^2 \frac{2x.dx}{x^{2}+1}$and got really confused what happens to the limits when you use change of variable say $t=x^{2}+1$

2. If you can see that the derivative of $x^2 + 1$ is $2x$, you don't need to change your limits. However, if you really want to change it, remember that the limits are just values for x. So:

because
$t = x^2 + 1$
when $x = 0, t = 1$
when $x = 2, t = 5$