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

ok ive got to $\displaystyle \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 $\displaystyle t=x^{2}+1 $(Doh)

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- Jun 3rd 2008, 04:13 AMskystarconfused-integration problem-URGENT
$\displaystyle \int_0^2 \frac{(x+1)^2}{x^{2}+1} dx$

ok ive got to $\displaystyle \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 $\displaystyle t=x^{2}+1 $(Doh) - Jun 3rd 2008, 04:18 AMGusbob
If you can see that the derivative of $\displaystyle x^2 + 1$ is $\displaystyle 2x$, 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

$\displaystyle t = x^2 + 1$

when $\displaystyle x = 0, t = 1$

when $\displaystyle x = 2, t = 5$