# Math Help - double integrals problem

1. ## double integrals problem

Im doing this problem below:

here is the solution and i understand everything except how they integrated the r(sqrt(1+r^2)). could anyone point out how they accomplished that? Thank you.

solution:

2. $\displaystyle{\int 2r - r \sqrt{1+r^2} dr = \int 2r dr - \int r \sqrt{1+r^2} dr}$

$\displaystyle{\int 2r dr} = 2 \times \dfrac{r^2}{2} = r^2$

for $\displaystyle{ \int r \sqrt{1+r^2} dr}$ use substitution rule by supposing $u = 1+r^2$

So, $du = 2r \mbox{dr} \implies dr = \dfrac{du}{2}$

3. ah, i should of know that.
Thanks a bunch.