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:
$\displaystyle \displaystyle{\int 2r - r \sqrt{1+r^2} dr = \int 2r dr - \int r \sqrt{1+r^2} dr}$
$\displaystyle \displaystyle{\int 2r dr} = 2 \times \dfrac{r^2}{2} = r^2$
for $\displaystyle \displaystyle{ \int r \sqrt{1+r^2} dr}$ use substitution rule by supposing $\displaystyle u = 1+r^2$
So, $\displaystyle du = 2r \mbox{dr} \implies dr = \dfrac{du}{2}$